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Similar Question 1
<p>Determine the sum of the arithmetic series.</p><p><code class='latex inline'>a = 2, t_n = -34, n = 15</code></p>
Similar Question 2
<p>Write the first four terms of the following Sigma notation.</p><p><code class='latex inline'> \displaystyle \sum^{n}_{i = 1}\frac{(-6)^{i - 1}}{5^{n - 1}} </code></p>
Similar Question 3
<p>Determine the sum of each arithmetic series.</p><p><code class='latex inline'>\dfrac{1}{x^2} + \dfrac{4}{x^2} + \dfrac{7}{x^2} + ... + \dfrac{94}{x^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
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<p>Find the sum of each finite arithmetic series.</p><p><code class='latex inline'>\displaystyle 10+20+30+\cdots+110+120 </code></p>
<p>Write the first four terms of the following Sigma notation.</p><p><code class='latex inline'> \displaystyle \sum^{n}_{i = 1} 3^{-i}8^{i + 1} </code></p>
<p>The third term of an arithmetic sequence is 18 and the seventh term is 30. Find the sum of the first 23 terms.</p>
<p>Determine the sum of each geometric series.</p><p><code class='latex inline'>3 + 9 + 27 + ... + 6561</code></p>
<p>Determine the number of terms, <code class='latex inline'>n</code>, for each arithmetic series with the given sum.</p><p><code class='latex inline'>5 + 1 - 3 - ... - t_n = -345</code></p>
<p>Evaluate each infinite geometric series.</p><p><code class='latex inline'>\displaystyle 1.1+0.11+0.011+\ldots </code></p>
<p>Architecture In a 20 -row theater, the number of seats in a row increases by three with each successive row. The first row has 18 seats.</p><p>a. Write an arithmetic series to represent the number of seats in the theater.</p><p>b. Find the total seating capacity of the theater.</p><p>c. Front-row tickets for a concert cost <code class='latex inline'>\displaystyle \$ 60 </code>. After every 5 rows, the ticket price goes down by <code class='latex inline'>\displaystyle \$ 5 . </code> What is the total amount of money generated by a full house?</p>
<p>The first and last terms in each arithmetic series are given. Determine the sum of the series.</p><p><code class='latex inline'>a = 9, t_{9} = -\dfrac{1}{729}</code></p>
<p>Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified number of terms.</p><p><code class='latex inline'>\displaystyle 1+2+3+4+\ldots ; n=1000 </code></p>
<p>Determine whether each series is geometric, arithmetic, or neither. Justify your answer.</p><p><code class='latex inline'>\dfrac{1}{8} + \dfrac{1}{7} + \dfrac{1}{6} + \dfrac{1}{5} + ...</code></p>
<p>Evaluate each infinite geometric series.</p><p><code class='latex inline'>\displaystyle 1-\frac{1}{5}+\frac{1}{25}-\frac{1}{125}+\ldots </code></p>
<p>Determine the sum of each arithmetic series.</p><p><code class='latex inline'>\dfrac{1}{x^2} + \dfrac{4}{x^2} + \dfrac{7}{x^2} + ... + \dfrac{94}{x^2}</code></p>
<p>Cool Juices makes a profit of $350 in the first week of a 16-week summer season. After the first week, the profit increases by $75 per week.</p><p>a) Explain why the total profit for the season represents an arithmetic series.<br> b) Determine the total profit for the season</p>
<p>For each geometric series. determine the values of <code class='latex inline'>a</code> and <code class='latex inline'>r</code>. Then. determine the specified sum.</p><p><code class='latex inline'>S_{50}</code> for <code class='latex inline'>9 - 9 + 9 - ...</code></p>
<p>Determine <code class='latex inline'>S_n</code> for each geometric series.</p><p><code class='latex inline'>a = -2, r = 2, n = 13</code></p>
<p>Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified number of terms.</p><p><code class='latex inline'>\displaystyle -5+25-125+625-\ldots ; n=9 </code></p>
<p>Determine the sum of each geometric series. </p><p><code class='latex inline'>5 + 20 + 80 + ... + 20480</code></p>
<p>Determine whether each list is a sequence or a series and finite or infinite.</p><p><code class='latex inline'>\displaystyle 5+10+\cdots+25 </code></p>
<p>Determine <code class='latex inline'>S_n</code> for each geometric series.</p><p><code class='latex inline'>f(1) = 4, r = -2, n = 10</code></p>
<p>Write the following sum with sigma notation up to the nth term.</p><p><code class='latex inline'> \displaystyle \frac{\sqrt{1}}{1^2} + \frac{\sqrt{2}}{2^2} + \frac{\sqrt{3}}{3^2} + ... +\frac{\sqrt{n}}{n^2} </code></p>
<p>The first and last terms in each arithmetic series are given. Determine the sum of the series.</p><p><code class='latex inline'>a = -3, t_{36} = -73</code></p>
<p>Evaluate each infinite geometric series.</p><p><code class='latex inline'>\displaystyle 3+2+\frac{4}{3}+\frac{8}{9}+\ldots </code></p>
<p>For each geometric series. determine the values of <code class='latex inline'>a</code> and <code class='latex inline'>r</code>. Then. determine the specified sum.</p><p><code class='latex inline'>S_8</code> for <code class='latex inline'>\dfrac{1}{8} + \dfrac{1}{4} + \dfrac{1}{2} + ...</code></p>
<p>Determine whether each infinite geometric series diverges or converges. If the series converges, state the sum.</p><p><code class='latex inline'>\displaystyle 1+2+4+\ldots </code></p>
<p>Evaluate each finite geometric series.</p><p><code class='latex inline'>\displaystyle 9-6+4-\frac{8}{3}+\frac{16}{9} </code></p>
<p>The general term and the sum of the first <code class='latex inline'>n</code> terms of each arithmetic series is given. Determine the value of <code class='latex inline'>n</code>.</p><p><code class='latex inline'>t_n = 2n - 1; S_n = 1234321</code></p>
<p>Evaluate the sum of the finite geometric series.</p><p><code class='latex inline'>\displaystyle 3+6+12+24+48+\cdots+768 </code></p>
<p>Determine the sum of each arithmetic series.</p><p><code class='latex inline'>-8\sqrt{6} - 6\sqrt{6} - 4\sqrt{6} - ... + 34\sqrt{6}</code></p>
<p>Determine whether each series is geometric, arithmetic, or neither. Justify your answer.</p><p><code class='latex inline'>6 + 12 + 18 + 24 + ...</code></p>
<p>Find the specified sum for each arithmetic series. </p><p><code class='latex inline'>S_{18}</code> for 1$\dfrac{2}{3} + 1 + \dfrac{4}{3}$` + ...</p>
<p>Determine whether each infinite geometric series diverges or converges. If the series converges, state the sum.</p><p><code class='latex inline'>\displaystyle 1+\frac{1}{5}+\frac{1}{25}+\ldots </code></p>
<p>Grades A student has taken three math tests so far this semester. His scores for the first three tests were 75,79 , and 83 .</p><p>a. Suppose his test scores continue to improve at the same rate. What will be his grade on the sixth (and final) test?</p><p>b. What will be his total score for all six tests?</p>
<p>Write each arithmetic series in summation notation.</p><p><code class='latex inline'>\displaystyle 100+90+80+\cdots+10 </code></p>
<p>The first and last terms in each arithmetic series are given. Determine the sum of the series.</p><p><code class='latex inline'>a = 6.6, t_{23} = -19.8</code></p>
<p>Determine the number of terms, <code class='latex inline'>n</code>, for each arithmetic series with the given sum.</p><p><code class='latex inline'>-30 - 26 - 22 - ... - t_n = -120</code></p>
<p>For each geometric series. determine the values of <code class='latex inline'>a</code> and <code class='latex inline'>r</code>. Then. determine the specified sum.</p><p><code class='latex inline'>S_9</code> for <code class='latex inline'>3 + 6 + 12 + ...</code></p>
<p>Determine the sum of each arithmetic series. </p><p>-20 - 18 - 16 - ... - 2</p>
<p>Write the first four terms of the following Sigma notation.</p><p><code class='latex inline'> \displaystyle \sum^{n}_{i = 1}\frac{(-6)^{i - 1}}{5^{n - 1}} </code></p>
<p>Find the specified sum for each arithmetic series. </p><p><code class='latex inline'>S_{21}</code> for a + (2a + b) + (3a + 2b) + ...</p>
<p>Determine the sum of each arithmetic series. </p><p>1 + 5 + 9 + ... + 77</p>
<p>Determine the sum of the arithmetic series.</p><p><code class='latex inline'>a = 7x, t_n = 32x, n = 17</code></p>
<p>Determine whether each series is geometric, arithmetic, or neither. Justify your answer.</p><p><code class='latex inline'>6571 - 2187 + 729 - 243 + ...</code></p>
<p>Determine the sum of each geometric series. </p><p><code class='latex inline'>3 + 9 + 27 + ... + 59049</code></p>
<p>Determine the sum of each arithmetic series. </p><p>5 + 10 + 15 + ... + 265</p>
<p>Find the specified sum for each arithmetic series. </p><p><code class='latex inline'>S_{11}</code> for 2 + 10 + 18 + ...</p>
<p>Write the following sum with sigma notation up to the nth term.</p><p><code class='latex inline'> \displaystyle 2 + 4 + 6 + ... + 20 </code></p>
<p>Write each arithmetic series in summation notation.</p><p><code class='latex inline'>\displaystyle 1+5+9+\cdots+41+45 </code></p>
<p>Determine the sum of each arithmetic series. </p><p>4 + 2.5 + 1 + ... - 33.5</p>
<p>Which are arithmetic series? Justify your answers.</p><p><code class='latex inline'>-\dfrac{8}{b} + \dfrac{4}{b} - \dfrac{2}{b} + ...</code></p>
<p>Determine the sum of each arithmetic series. </p><p><code class='latex inline'>\sqrt{3} + 2\sqrt{3} + 3\sqrt{3} + ... + 20\sqrt{3}</code></p>
<p>Find the specified sum for each arithmetic series. </p><p><code class='latex inline'>S_{10}</code> for 1 + 6 + 11 + ...</p>
<p>Determine <code class='latex inline'>S_n</code> for each geometric series.</p><p><code class='latex inline'>a = \dfrac{1}{81}, r = 3, n = 7</code></p>
<p>The function <code class='latex inline'>\displaystyle S(n)=\frac{10\left(1-0.8^{n}\right)}{0.2} </code> represents the sum of the first <code class='latex inline'>\displaystyle n </code> terms of an infinite geometric series.</p><p>a. What is the domain of the function?</p><p>b. Find <code class='latex inline'>\displaystyle S(n) </code> for <code class='latex inline'>\displaystyle n=1,2,3, \ldots, 10 . </code> Sketch the graph of the function.</p><p>c. Find the sum <code class='latex inline'>\displaystyle S </code> of the infinite geometric series.</p>
<p>Determine the number of terms, <code class='latex inline'>n</code>, for each arithmetic series with the given sum.</p><p><code class='latex inline'>19 + 15 + 11 + ... - t_n = -441</code></p>
<p>Determine <code class='latex inline'>S_n</code> for each geometric series.</p><p><code class='latex inline'>a = 16, r = 2, n = 13</code></p>
<p>Write the first four terms of the following Sigma notation.</p><p><code class='latex inline'> \displaystyle \sum^{n}_{i = 1}\frac{(-3)^{i - 1}}{4^i} </code></p>
<p>Determine <code class='latex inline'>S_n</code> for each geometric series.</p><p><code class='latex inline'>f(1) = 0.4, r = 1.5, n = 6</code></p>
<p>Find the sum of each finite arithmetic series.</p><p><code class='latex inline'>\displaystyle 5+6+7+\cdots+11 </code></p>
<p>For each geometric series. determine the values of <code class='latex inline'>a</code> and <code class='latex inline'>r</code>. Then. determine the specified sum.</p><p><code class='latex inline'>S_{12}</code> for <code class='latex inline'>5 - 10 + 20 - ...</code></p>
<p>Determine whether each infinite geometric series diverges or converges.</p><p><code class='latex inline'>\displaystyle \frac{1}{64}+\frac{1}{32}+\frac{1}{16}+\ldots </code></p>
<p>The sum of an infinite geometric series is twice its first term.</p><p>a. Error Analysis A student says the common ratio of the series is <code class='latex inline'>\displaystyle \frac{3}{2} </code>. What is the student&#39;s error?</p><p>b. Find the common ratio of the series.</p>
<p>Determine the sum of each geometric series.</p><p><code class='latex inline'>2 + 1 + \dfrac{1}{2} + ... + \dfrac{1}{128}</code></p>
<p>Determine the sum of each arithmetic series. </p><p>-17 - 10 - 3 - ... + 74</p>
<p>Determine the sum of the first 10 terms of a geometric series with common ratio 2 and whose tenth term is 16.</p>
<p>Find the specified sum for each arithmetic series. </p><p><code class='latex inline'>S_{20}</code> for 100 + 85 + 70 + ...</p>
<p>The general term and the sum of the first <code class='latex inline'>n</code> terms of each arithmetic series is given. Determine the value of <code class='latex inline'>n</code>.</p><p><code class='latex inline'>t_n = 3n - 1; S_n = 950</code></p>
<p>Write the following sum with sigma notation up to the nth term.</p><p><code class='latex inline'> \displaystyle 1 + 3x + 5x^2 + 7x^3 + ... +101x^{50} </code></p>
<p>Determine whether each series is geometric, arithmetic, or neither. Justify your answer.</p><p><code class='latex inline'>1 + 10 + 100 + ...</code></p>
<p>Determine the sum of each arithmetic series. </p><p>2 + 4 + 6 + ... + 2000</p>
<p>Determine the sum of each geometric series. </p><p><code class='latex inline'>1 + 5 + 25 + ... + 3125</code></p>
<p>For each arithmetic series, state the values of <code class='latex inline'>a</code> and of <code class='latex inline'>d</code>. Then, determine the sum of the first 10 terms. </p><p>5 + 12 + 19 + ...</p>
<p>The sum of the first 5 terms of an arithmetic sequence is 625 and the sum of the first 10 terms is 100. Determine the sum of the first 15 terms.</p>
<p>Bianca has a choice between two summer jobs, each for a period of 16 weeks.</p><p><em>Job A</em>: He would be paid $450 every two weeks.</p><p><em>Job B</em>: He would be paid $100 the first week and then an additional $25 per week for each successive week.</p><p>Which job should Bashira accept to earn the most money? Justify your answer.</p>
<p>For each arithmetic series, state the values of <code class='latex inline'>a</code> and of <code class='latex inline'>d</code>. Then, determine the sum of the first 10 terms. </p><p>3 + 7 + 11 + ...</p>
<p>Determine the sum of the arithmetic series.</p><p><code class='latex inline'>a = 2, t_n = -34, n = 15</code></p>
<p>Determine the number of terms, <code class='latex inline'>n</code>, for each arithmetic series with the given sum.</p><p><code class='latex inline'>10 + 8 + 6 + ... + t_n = -350</code></p>
<p>Determine the number of terms, <code class='latex inline'>n</code>, for each arithmetic series with the given sum.</p><p><code class='latex inline'>1 + 2 + 3 + ... + t_n = 78</code></p>
<p>In <code class='latex inline'>\triangle ABC, \angle A = 56^o</code>, <code class='latex inline'>\angle B = 64^o</code>, and <code class='latex inline'>c = 6.0</code> cm. What is the length of side <code class='latex inline'>a</code>?</p><p>A. 5.7 cm</p><p>B. 6.3 cm</p><p>C. 0.5 cm</p><p>D. 0.96 cm</p>
<p>Find an expression for the sum of the first <code class='latex inline'>n</code> terms of the series with the given general term. Then, use your expression to find the sum when <code class='latex inline'>n</code> = 9.</p><p><code class='latex inline'>t_n = -2(3)^{n-1}</code></p>
<p>Determine <code class='latex inline'>S_n</code> for each geometric series.</p><p><code class='latex inline'>a = -4, r = -1, n = 20</code></p>
<p>Find the specified sum for each arithmetic series. </p><p><code class='latex inline'>S_{15}</code> for 2 - 1 - 4 - ...</p>
<p>Determine the sum of the arithmetic series.</p><p><code class='latex inline'>a = 14, d = -3, n = 16</code></p>
<p>Determine whether each infinite geometric series diverges or converges. If the series converges, state the sum.</p><p><code class='latex inline'>\displaystyle -54-18-6-\ldots </code></p>
<p>Determine whether each series is geometric, arithmetic, or neither. Justify your answer.</p><p><code class='latex inline'>7 - 8 - 10 - 13 - ...</code></p>
<p>Use the formula for the sum of an infinite geometric series to show that <code class='latex inline'>\displaystyle 0 . \overline{9}=1 </code>.</p>
<p>Determine the sum of the arithmetic series.</p><p><code class='latex inline'>a = -1, t_n = 11, n = 21</code></p>
<p>Determine the number of terms, <code class='latex inline'>n</code>, for each arithmetic series with the given sum.</p><p><code class='latex inline'>15 + 20 + 25 + ... + t_n = 1250</code></p>
<p>Determine the sum of each arithmetic series.</p><p><code class='latex inline'>53x + 47x + 41x - ... - 55x</code></p>
<p>Determine <code class='latex inline'>S_n</code> for each geometric series.</p><p><code class='latex inline'>f(1) = -6, r = 4, n = 9</code></p>
<p>Determine whether each infinite geometric series diverges or converges. If the series converges, state the sum.</p><p><code class='latex inline'>\displaystyle 1-\frac{1}{2}+\frac{1}{4}-\ldots </code></p>
<p>Determine the sum of each arithmetic series. </p><p>2 + 7 + 12 + ... + 62</p>
<p>Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified number of terms.</p><p><code class='latex inline'>\displaystyle 2+4+8+16+\ldots ; n=10 </code></p>
<p>Determine the sum of the arithmetic series.</p><p><code class='latex inline'>a = 3, t_{n} = 15, n = 8</code></p>
<p>Write the following sum with sigma notation up to the nth term.</p><p><code class='latex inline'> \displaystyle \frac{1}{2\ln 2} - \frac{1}{3\ln 3} + \frac{1}{4 \ln 4} - ... + \frac{1}{100 \ln 100 } </code></p>
<p>Find the specified sum for each arithmetic series. </p><p><code class='latex inline'>S_{16}</code> for 3 + 7 + 11 + ...</p>
<p>For each geometric series. determine the values of <code class='latex inline'>a</code> and <code class='latex inline'>r</code>. Then. determine the specified sum.</p><p><code class='latex inline'>S_17</code> for <code class='latex inline'>2 + 0.2 + 0.02 + ...</code></p>
<p>Determine the sum of each geometric series. </p><p><code class='latex inline'>3\sqrt{6} - 18 + 18\sqrt{6} - ... + 839808\sqrt{6}</code></p>
<p>Determine whether each series is geometric, arithmetic, or neither. Justify your answer.</p><p><code class='latex inline'>-4 + 8 - 16 + 32 - ...</code></p>
<p>Determine <code class='latex inline'>S_n</code> for each geometric series.</p><p><code class='latex inline'>f(1) = 6, r = -\dfrac{1}{2}, n = 11</code></p>
<p>Find the specified value for each infinite geometric series.</p><p>a. <code class='latex inline'>\displaystyle a_{1}=12, S=96 ; </code> find <code class='latex inline'>\displaystyle r </code></p><p>b. <code class='latex inline'>\displaystyle S=12, r=\frac{1}{6} ; </code> find <code class='latex inline'>\displaystyle a_{1} </code></p>
<p>Write the following sum with sigma notation up to the nth term.</p><p><code class='latex inline'> \displaystyle 1 - 2x + 3x^2 - 4x^3 + 5x^4 + .... - 100x^{99} </code></p>
<p>Determine whether each infinite geometric series diverges or converges. If the series converges, state the sum.</p><p><code class='latex inline'>\displaystyle \frac{1}{4}+\frac{1}{2}+1+2+\ldots </code></p>
<p>Determine the sum of the arithmetic series.</p><p><code class='latex inline'>a = \dfrac{4}{3}, d = \dfrac{1}{4}, n = 8</code></p>
<p>Determine the sum of each arithmetic series. </p><p><code class='latex inline'>-2 - 8 - 14 - ... - 128</code></p>
<p>Determine the sum of each geometric series. </p><p><code class='latex inline'>\dfrac{1}{3} + 1 + 3 + ... + 6561</code></p>
<p>Find the specified sum for each arithmetic series. </p><p><code class='latex inline'>S_{15}</code> for 5 + 9 + 13 + ...</p>
<p>Determine the number of terms, <code class='latex inline'>n</code>, for each arithmetic series with the given sum.</p><p><code class='latex inline'>3 + 7 + 11 + ... + t_n = 1830</code></p>
<p>Find the specified sum for each arithmetic series. </p><p><code class='latex inline'>S_{20}</code> for -21 - 19 - 17 + ...</p>
<p>Determine the sum of each arithmetic series. </p><p>4 + 8 + 12 + ... + 400</p>
<p>For each geometric series. determine the values of <code class='latex inline'>a</code> and <code class='latex inline'>r</code>. Then. determine the specified sum.</p><p><code class='latex inline'>S_{13}</code> for <code class='latex inline'>-0.2 + 0.6 - 1.8 + ...</code></p>
<p>Evaluate the sum of the finite geometric series.</p><p><code class='latex inline'>\displaystyle 1+2+4+8+\cdots+128 </code></p>
<p>Determine the sum of each arithmetic series.</p><p><code class='latex inline'>(9a - 5b) + (12a - 4b) + (15a - 3b) + ... + (93a + 23b)</code></p>
<p>Write the first four terms of the following Sigma notation.</p><p><code class='latex inline'> \displaystyle \sum^{n}_{i = 1} \frac{4^{i + 1}}{5^i} </code></p>
<p>The first and last terms in each arithmetic series are given. Determine the sum of the series.</p><p><code class='latex inline'>a = -\sqrt{5}, t_{24} = 15\sqrt{5}</code></p>
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