9. Q9d
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Similar Question 1
<p>Use the given recursion formula to determine the first five terms of each sequence.</p><p><code class='latex inline'>t_1 = -1</code>,</p><p><code class='latex inline'>t_2 = 4</code>,</p><p><code class='latex inline'>t_n = -2t_{n - 2} + t_{n - 1}</code></p>
Similar Question 2
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 = -5, t_n = 4-2t_{n-1}</code></p>
Similar Question 3
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>f(1) = 8, f(n) = \frac{f(n-1)}{2}</code></p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Given the recursion formula, write the first four terms of the sequence and then determine the explicit formula for the sequence.</p><p><code class='latex inline'>t_1 = 81</code>,</p><p><code class='latex inline'>t_n = -\dfrac{1}{3}t_{n - 1}</code></p>
<p>Write the first four terms of each sequence.</p><p><code class='latex inline'>t_1 = -3</code>,</p><p><code class='latex inline'>t_n = -5t_{n - 1}</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 = -5, t_n = 4-2t_{n-1}</code></p>
<p>Write the first four terms of each sequence.</p><p><code class='latex inline'>f(1) = 64</code>,</p><p><code class='latex inline'>f(n) = \dfrac{f(n - 1)}{-4}</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 = 4</code>,</p><p><code class='latex inline'>t_n = 3t_{n - 1} - 2</code></p>
<p>Given the explicit formula of a sequence, write the first four terms and then determine a recursion formula for each sequence.</p><p><code class='latex inline'>\displaystyle t_n = 3n + 1</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 =4, t_n =t_{n -1}+3</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>f(1) = 8, f(n) = \frac{f(n-1)}{2}</code></p>
<p>What is an explicit formula for the sequence <code class='latex inline'>\displaystyle 5,8,11,14, \ldots ? </code></p>
<p>Write an explicit and a recursive formula for each sequence.</p><p><code class='latex inline'>\displaystyle -5,-4,-3,-2,-1, \ldots </code></p>
<p>For each graph, write the sequence of terms and determine a recursion formula using function notation.</p><img src="/qimages/23304" />
<p>Write the first four terms of each sequence.</p><p><code class='latex inline'>t_1 = -2</code>,</p><p><code class='latex inline'>t_n = 11 + 3t_{n - 1}</code></p>
<p>Use the given recursion formula to determine the first four terms of each sequence. Then, use words to describe the rule for determining terms in the sequence.</p><p><code class='latex inline'>\displaystyle t_1= -2, t_2 = 3, t_n = 3t_{n-2} + t_{n - 1}</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 = 90</code>,</p><p><code class='latex inline'>t_n = \dfrac{4t_{n-1}}{3}</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 =1, t_n = (t_{n-1})^2 + 3n</code></p>
<p>Determine whether each formula is explicit or recursive. Then find the first five terms of each sequence.</p><p><code class='latex inline'>\displaystyle a_{n}=3 n(n+1) </code></p>
<p>Given the recursion formula, write the first four terms of the sequence and then determine the explicit formula for the sequence.</p><p><code class='latex inline'>\displaystyle t_1 = 1, t_n = \frac{1}{2}t_{n - 1}</code></p>
<p>Given the explicit formula of a sequence, write the first four terms and then determine a recursion formula for each sequence.</p><p><code class='latex inline'>\displaystyle f(n) = (n - 2)(n + 2)</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 = \frac{1}{2}, t_n=4t_{n-1} + 2</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 = 2</code>,</p><p><code class='latex inline'>t_n = t_{n - 1} + 6</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 = 50, t_n = \frac{t_{n -1}}{2}</code></p>
<p>Determine a recursion formula for each sequence.</p><p>-2, -3, -5, -8, ...</p>
<p>Write the first five terms of each sequence, starting at <code class='latex inline'>f(1)</code>.</p><p><code class='latex inline'>f(2) = -5</code>,</p><p><code class='latex inline'>f(n) = -3f(n - 1) + 1</code></p>
<p>A square-based pyramid with height 7 m is constructed with cubic blocks measuring 1 m on each side.</p><img src="/qimages/1128" /><p>Write a recursion formula for the sequence that represents the number of blocks used at each level from the top down.</p>
<p>Fibonacci sequence is: <code class='latex inline'>1, 1, 2, 3, 5, 8, 13, 21</code>, ...</p><p>a) Find the next three terms and a formation rule for this sequence.</p><p>b) Examine the ratios of successive terms of the Fibonacci sequence <code class='latex inline'> \displaystyle \frac{(n + 1)\text{th term}}{n\text{th term}} </code>. Conjecture a possible value for the ratio <code class='latex inline'> \displaystyle \frac{1000 \text{th term}}{999 \text{th term}} </code>.</p>
<p>Determine a recursion formula for each sequence.</p><p><code class='latex inline'>5 ,11, 17, 23, ...</code></p>
<p>Vocabulary Explain the difference between an explicit formula and a recursive definition. Give an example of each.</p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 = 8, t_n = 2n - 36_{n-1}</code></p>
<p>For each graph, write the sequence of terms and determine a recursion formula using function notation.</p><img src="/qimages/23305" />
<p>An example of a constant sequence is <code class='latex inline'>206, 206, 206, ... </code>. Write a recursion formula for this sequence. Write another constant sequence formula.</p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>f(1) = 9, f(n) = f(n-1) -2</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 = 100, t_n = \frac{5t_{n-1}}{0.1}</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>f(1) = 18, f(n) = f(n-1) + 2</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>f(1) = 25, f(n) = -0.5f(n-1)</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>f(1) = 4</code>,</p><p><code class='latex inline'>f(n) = \dfrac{f(n - 1)}{n + 1}</code></p>
<p>Write an explicit and a recursive formula for each sequence.</p><p><code class='latex inline'>\displaystyle 27,15,3,-9,-21, \ldots </code></p>
<p>Given the recursion formula, write the first four terms of the sequence and then determine the explicit formula for the sequence.</p><p><code class='latex inline'>\displaystyle t_1 = 10, t_n = t_{n - 1} - 10</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>f(1) = -1, f(n) = -3f(n-1)</code></p>
<p>What is a recursive definition for the sequence <code class='latex inline'>\displaystyle 3,6,12,24, \ldots ? </code></p>
<p>Given the explicit formula of a sequence, write the first four terms and then determine a recursion formula for each sequence.</p><p><code class='latex inline'>\displaystyle f(n) = 2(4)^{n-1}</code></p>
<p>Write the first five terms of each sequence, starting at <code class='latex inline'>f(1)</code>.</p><p><code class='latex inline'>f(3) = 7</code>,</p><p><code class='latex inline'>f(n) = f(n - 1) - 2n</code></p>
<p>Use the given recursion formula to determine the first five terms of each sequence.</p><p><code class='latex inline'>t_1 = 5</code>,</p><p><code class='latex inline'>t_2 = 1</code>,</p><p><code class='latex inline'>t_3 = -1</code>,</p><p><code class='latex inline'>t_n = t_{n - 3} - 2t_{n - 2} + t_{n - 1}</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 = 3</code>,</p><p><code class='latex inline'>t_n = 3n - 2t_{n - 1}</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1=3, t_n = 2t_{n - 1}</code></p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 = 500</code>,</p><p><code class='latex inline'>t_n = \dfrac{t_{n-1}}{5}</code></p>
<p>For each graph, write the sequence of terms and determine a recursion formal using function notation.</p><img src="/qimages/1125" />
<p>Given the recursion formula, write the first four terms of the sequence and then determine the explicit formula for the sequence.</p><p><code class='latex inline'>\displaystyle t_{1} = -2, t_n=t_{n - 1} -\frac{1}{n(n - 1)}</code></p>
<p>Sam and Michelle paid $<code class='latex inline'>250\ 000</code> for their first home. The real estate agent told them that the house will appreciate in value by <code class='latex inline'>3</code>% per year.</p><p><strong>(a)</strong> Copy and complete the table to show the value of the house for the next <code class='latex inline'>10</code> years.</p><img src="/qimages/1126" /><p><strong>(b)</strong> Write the value of the house for the first <code class='latex inline'>10</code> years as a sequence.</p><p><strong>(c)</strong> Write a recursion formula to represent the value of the house Use your formula to predict the value after 15 years.</p> <p>Given the explicit formula of a sequence, write the first four terms and then determine a recursion formula for each sequence.</p><p><code class='latex inline'>\displaystyle f(n) = 3^{-n}</code></p> <p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>f(1) = -1.5</code>,</p><p><code class='latex inline'>f(n) = f(n - 1) + n</code></p> <p>Given the recursion formula, write the first four terms of the sequence and then determine the explicit formula for the sequence.</p><p><code class='latex inline'>t_1 = 0</code>,</p><p><code class='latex inline'>t_n = t_{n - 1} + 2n -1</code></p> <p>Determine whether each formula is explicit or recursive. Then find the first five terms of each sequence.</p><p><code class='latex inline'>\displaystyle a_{n}=-3 a_{n-1} </code>, where <code class='latex inline'>\displaystyle a_{1}=-2 </code></p> <p>Determine whether each formula is explicit or recursive. Then find the first five terms of each sequence.</p><p><code class='latex inline'>\displaystyle a_{1}=-121, a_{n}=a_{n-1}+13 </code></p> <p>Find the arithmetic mean <code class='latex inline'>\displaystyle a_{n} </code> of the given terms.</p><p><code class='latex inline'>\displaystyle a_{n-1}=0.3, a_{n+1}=1.9 </code></p> <p>Write the first four terms of each sequence.</p><p><code class='latex inline'>f(1) = a - 2b</code>,</p><p><code class='latex inline'>f(n) = f(n - 1) + 3b</code></p> <p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>f(1) = -3</code>,</p><p><code class='latex inline'>f(n) = f(n - 1) + 4</code></p> <p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>f(1) = 25, f(n) = -0.5f(n-1)</code></p> <p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 = -3, t_n = 0.22t_{n -1}-1.2</code></p> <p>Given the explicit formula of a sequence, write the first four terms and then determine a recursion formula for each sequence.</p><p> <code class='latex inline'>\displaystyle t_n = (2n- 1)^2</code></p> <p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>f(1)=3, f(n) = \frac{f(n-1)}{n}</code></p> <p>Write an explicit and a recursive formula for each sequence.</p><p><code class='latex inline'>\displaystyle -5,-3.5,-2,-0.5,1, \ldots </code></p> <p>Use the given recursion formula to determine the first four terms of each sequence. Then, use words to describe the rule for determining terms in the sequence.</p><p><code class='latex inline'>\displaystyle f(1) =2, f(2) = 2, f(n) = f(n -1) + 2f(n -2)</code></p> <p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>f(1) =3, f(n)= f(n-1) + 2</code></p> <p>A new theatre is being built for a youth orchestra. This theatre has 50 seats in the first row, 54 in the second row, 62 in the third row, 74 in the next row, and so on.</p><p><strong>(a)</strong> Represent the number of seats i the rows as a sequence.</p><p><strong>(b)</strong> Describe the pattern in the number of seats per row.</p><p><strong>(c)</strong> Write a recursion formula to represent the number of seats in any row.</p> <p>Determine a recursion formula for each sequence.</p><p>2, 5, 11, 23, ...</p> <p>Use the given recursion formula to determine the first five terms of each sequence.</p><p><code class='latex inline'>t_1 = 3</code>,</p><p><code class='latex inline'>t_2 = -2</code>,</p><p><code class='latex inline'>t_n = t_{n - 2} \times t_{n - 1} + n</code></p> <p>Use the given recursion formula to determine the first five terms of each sequence.</p><p><code class='latex inline'>t_1 = -1</code>,</p><p><code class='latex inline'>t_2 = 4</code>,</p><p><code class='latex inline'>t_n = -2t_{n - 2} + t_{n - 1}</code></p> <p>For each graph, write the sequence of terms and determine a recursion formal using function notation.</p><img src="/qimages/1124" /> <p>Given the recursion formula, write the first four terms of the sequence and then determine the explicit formula for the sequence.</p><p><code class='latex inline'>\displaystyle t_1 = 3, t_n = 2t_{n -1} + 1</code></p> <p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>f(1) = -7</code>,</p><p><code class='latex inline'>f(n) = -f(n - 1) + 3</code></p> <p>Determine a recursion formula for each sequence.</p><p><code class='latex inline'>4, 1, -2, -5, ...</code></p> <p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 = -1</code>,</p><p><code class='latex inline'>t_n = 0.5t_{n - 1} + 0.5</code></p> <p>Given the explicit formula of a sequence, write the first four terms and then determine a recursion formula for each sequence.</p><p> <code class='latex inline'>\displaystyle t_n = \frac{n^2 + 1}{n}</code></p> <p>Use the given recursion formula to determine the first four terms of each sequence. Then, use words to describe the rule for determining terms in the sequence.</p><p><code class='latex inline'>\displaystyle f(1) = 1, f(2) =2, f(n) =f(n - 1)f(n-2)</code></p> <p>Write an explicit and a recursive formula for each sequence.</p><p><code class='latex inline'>\displaystyle 1,1 \frac{1}{3}, 1 \frac{2}{3}, 2, \ldots </code></p> <p>Determine a recursion formula for each sequence.</p><p><code class='latex inline'>4, 8, 16, 32, ...</code></p> <p>Annette and Gordon paid$275 000 for a new home. They were told that they can expect the house to appreciate in value by 3.5% per year.</p><p>a) Express 3.5% as a decimal.</p><p>b) Copy and complete the table to show the value of the house for the next 8 years.</p><img src="/qimages/23306" /><p>c) Write the value of the house for the first 8 years as a sequence.</p><p>d) Write a recursion formula to represent the value of the house.</p><p>e) Use your formula in part d) to predict the value after 20 years.</p>
<p>A sequence has a first term of <code class='latex inline'>-8</code>. Each succeeding term is <code class='latex inline'>4</code> more than twice the previous term.</p><p><strong>(a)</strong> Write the first four terms of this sequence.</p><p><strong>(b)</strong> Define the sequence using a recursion formula and then graph the sequence.</p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>t_1 =7, t_n = 2t_{n -1}-1</code></p>
<p>Determine a recursion formula for each sequence.</p><p>3, -1, -7, -15, ...</p>
<p>Write the first four terms of each sequence, where <code class='latex inline'>n \in \mathbb{N}</code>.</p><p><code class='latex inline'>f(1) = 0.25</code>,</p><p><code class='latex inline'>f(n) = -2f(n - 1)</code></p>
<p>Use the given recursion formula to determine the first five terms of each sequence.</p><p><code class='latex inline'>t_1 = 2</code>,</p><p><code class='latex inline'>t_2 = 3</code>,</p><p><code class='latex inline'>t_n = 3t_{n - 2} - t_{n - 1}</code></p>
<p>The diagrams show the diagonals in regular polygons with n sides. Write the sequence for the number of diagonals and determine the recursion formula for this sequence.</p><img src="/qimages/1127" />
<p>Write an explicit and a recursive formula for each sequence.</p><p><code class='latex inline'>\displaystyle 2,4,6,8,10, \ldots </code></p>
<p>Determine a recursion formula for each sequence.</p><p><code class='latex inline'>-4, -2, -1, -\frac{1}{2}, ...</code></p>
<p>Use the given recursion formula to determine the first four terms of each sequence. Then, use words to describe the rule for determining terms in the sequence.</p><p><code class='latex inline'>\displaystyle t_1= 5, t_2 = 7, t_n = t_{n-2} - t_{n - 1}</code></p>
<p>Use the given recursion formula to determine the first four terms of each sequence. Then, use words to describe the rule for determining terms in the sequence.</p><p><code class='latex inline'>\displaystyle t_1= 1, t_2 = -4, t_n = t_{n-2} \times t_{n - 1}</code></p>
<p>Write the first four terms of each sequence.</p><p><code class='latex inline'>f(1) = 2c + 3d</code>,</p><p><code class='latex inline'>f(n) = f(n - 1) - c</code></p>
<p>Determine a recursion formula for each sequence.</p><p><code class='latex inline'>-5, 15, -45, 135, ...</code></p>
<p>Use the given recursion formula to determine the first five terms of each sequence.</p><p><code class='latex inline'>f(1) = 1</code>,</p><p><code class='latex inline'>f(2) = 1</code>,</p><p><code class='latex inline'>f(n) = f(n - 1) + f(n - 2)</code></p>
<p>Use the given recursion formula to determine the first five terms of each sequence.</p><p><code class='latex inline'>f(1) = 4</code>,</p><p><code class='latex inline'>f(2) = -1</code>,</p><p><code class='latex inline'>f(n) = f(n - 1) - 2f(n - 2)</code></p>
<p>Write the first four terms of each sequence.</p><p><code class='latex inline'>f(1) = m - 5n</code>,</p><p><code class='latex inline'>f(n) = f(n - 1) + 2m + n</code></p>
<p>Find the arithmetic mean <code class='latex inline'>\displaystyle a_{n} </code> of the given terms.</p><p><code class='latex inline'>\displaystyle a_{n-1}=-2 x, a_{n+1}=2 x </code></p>
<p>Given the recursion formula, write the first four terms of the sequence and then determine the explicit formula for the sequence.</p><p><code class='latex inline'>t_1 = 4</code>,</p><p><code class='latex inline'>t_n = t_{n - 1} - 7</code></p>
<p>Determine whether each formula is explicit or recursive. Then find the first five terms of each sequence.</p><p><code class='latex inline'>\displaystyle a_{n}=2 a_{n-1}+3 </code>, where <code class='latex inline'>\displaystyle a_{1}=3 </code></p>
<p>Write the first four terms of each sequence.</p><p><code class='latex inline'>t_1 = 1</code>,</p><p><code class='latex inline'>t_n = 1 - (t_{n - 1})^2</code></p>
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