Determine the sum of each arithmetic series.

• a=4, t_n=9, n=6

• a=10, d=-2, n=12

• a=7, t_n=-22, n=12

Determine the sum of each arithmetic series.

• a=-4, t_n=17, n=20

• \displaystyle{a=\frac{1}{3}}, \displaystyle{-\frac{1}{2}}, n=7

• a=3x, t_n=21x, n=15

For each arithmetic series, state the values of a and d. Then, determine the sum of the first 20 terms.

• 5+9+13+...

• 20+25+30+...

• 45+39+33+...

For each arithmetic series, state the values of a and d. Then, determine the sum of the first 20 terms.

• 2+2.2+2.4+...

• \displaystyle{\frac{1}{2}+\frac{3}{4}+1+...}

• -5-6-7-...

The first and last terms in each arithmetic series are given. Determine the sum of the series.

• \displaystyle{a=\frac{1}{2}}, t_8=4

• a=19, t_{12}=151

• a=-5, t_{45}=17

• a=11, t_{20}=101

Determine the sum of each arithmetic series.

(a) 6+13+20+...+69

(b) 4+15+26+...+213

(c) 5-8-21-...-190

(d) 100+90+80+...-100

Determine the sum of each arithmetic series.

• -1+2+5+...+164

• 2-5-12-...-222

• 21.5+14.2+6.9+...-715.8

• \displaystyle{\frac{5}{3}+\frac{11}{3}+\frac{17}{3}+...+\frac{53}{3}}

The 15th term in an arithmetic sequence is 43 and the sum of the first 15 terms of the series is 120. Determine the first three terms of the sequence.

In an arithmetic sequence of 50 terms, the 17th term is 53 and the 28th term is 86. Determine the sum of the first 50 terms of the corresponding arithmetic series.

Determine the sum of each arithmetic series.

• 2\sqrt{7}+5\sqrt{7}+8\sqrt{7}+...+83\sqrt{7}

• x-2x-5x-...-56x

• (5a-3b)+(4a-2b)+(3a-b)+...+(-5a+7b)

• \displaystyle{\frac{2}{x}+\frac{11}{20}+\frac{27}{20}+...}

Which are arithmetic series? Justify your answers.

(a) -2-8-11-17- ...

(b) 2x^2 + 3x^2 + 4x^2 + ...

(c) a + (a + 2b) + (a + 4b)+ ...

(d) \displaystyle{\frac{17}{20} + \frac{11}{20}+ \frac{27}{20}+ ...}

In a grocery store, apple juice cans are stacked in a triangular display. There are 5 cans in the top row and 12 cans in the bottom row. Each row has 1 can less than the previous row. How many cans are in the display?

A toy car is rolling down an inclined track and picking up speed as it goes. The car travels 4 cm in the first second, 8 cm in the second second, 12 cm in the next second, and so on. Determine the total distance travelled by the car in 30 s.

A snowball sentence is constructed so that each word has one more letter than the previous word. An example is, "I am not cold today."

• Determine the total number of letters in the sentence.
• Write your own snowball sentence and determine the number of letters in your sentence.

Determine an expression for the sum of the terms of an arithmetic series where the terms are represented by t_n=3n-2.

• Determine x so that 2x, 3x+1, and x^2+2 are the first three terms of an arithmetic sequence.

• Determine the sum of the first 10 terms of the sequence.

Sweet Treats finds that its profit increases by $200 per week throughout the 16 a €”week summer season. Sweet Treats profit is \$1200 in the first week.

(a) Explain why the total profit for the season is represented by an arithmetic series.

(b) Determine the total profit for the season.

How many terms in the series 5+9+13+...+t_n are less than 500? How many terms are needed for a sum of less than 500?

Two arithmetic sequences , 3, 9, 15, 21, ... and 4, 11, 18, 25, ..., share common terms. For example, 81 is a term in both sequences. What is the sum of the first 20 terms that these sequences have in common?

A. 8760

B. 8750

C. 8740

D. 8770

Find the sum of the series 1+2+4+5+7+8+10+11+...+2999.

What is the value of (1^2+3^2+...+171^2)-(2^2+4^2+6^2+...+170^2)?

Solve 6^{x-3}-6^{x-4}=1080.

A geometric sequence has 1 as its first term and 2n as its last. Show that if there are 2n terms, then the product of the terms of the sequence is (2n)^n.

Without using a calculator, determine the sum of the first 20 terms of the sequence \displaystyle{\frac{1}{2},\frac{1}{6},\frac{1}{12},\frac{1}{20}}, ...

** Arithmetic Series Formula **

\displaystyle S_n = \frac{n}{2} (2a + (n-1)d) = \frac{n}{2} (t_1 + t_n)

Arithmetic Series ex2

5 Arithmetic Series ex3

6 Find Series when given general term

7 Finding general term when given Series ex1

8 Finding general term when given Series ex2

9 Finding general term when given Series ex2