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Chapter 12: Q 12.35. (page 1181)

Find the sum of the first 30 terms of the arithmetic sequence: 5, 9, 13, 17, 21, 鈥�.

Short Answer

Expert verified

The obtained sum is 1890.

Step by step solution

01

Step 1. Given Information.

The arithmetic sequence is5,9,13,17,21,鈥�.

02

Step 2. Find the common difference d.

Find the common difference of consecutive terms.

d=9鈭�5=4

And, now find the 30th term of the sequence.

a30=5+30鈭�14=5+116=121

03

Step 3. Use the sum formula.

Use the sum formula Sn=n2a1+anto find the sum of the thirteenth term.

S30=3025+121=15126=1890

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Most popular questions from this chapter

an=鈭�1nn2.Write the first five terms of the sequence whose general term is

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

a1=4andr=3

Expand the partial sum and find its value:鈭�i=153i

Determine if each sequence is arithmetic. If so, indicate the common difference.

(a)鈭�4,4,2,10,8,16,鈥�(b)鈭�3,鈭�1,1,3,5,7,鈥�(c)7,2,鈭�3,鈭�8,鈭�13,鈭�18,鈥�

Find the eighteenth term of a sequence where the fifth term is 12 and the common difference is seven.
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