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Chapter 12: Q 126. (page 1185)

In your own words, explain how to find the sum of the first n terms of an arithmetic sequence without adding all the terms.

Short Answer

Expert verified

By using the arithmetic sequence sum formula, we can find the nth term sum.

Step by step solution

01

Step 1. Introduction.

If we have a sequence of nth terms. By substituting the first term and nth term value in the sum formula to find the nth term sum.

02

Step 2. Explanation.

Consider the sum formula of the nth term.

Sn=n2a1+an

Now, substitute the value of an as an=a1+n-1d.

Sn=n2a1+an=n2a1+a1+n-1d=n22a1+n-1d

Let's supposed that the first term is 4 and the value of d is 2.

Sn=n224+n-12=n2+n-1=n2+n

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Most popular questions from this chapter

Write the first five terms of the sequence whose general term isan=鈭�1n+1n3

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