Question

Find the indicated sum. Select your choice and click Submit to check your answer.

Given the arithmetic sequence 5, 8, 11..., evaluate summation of a sub n from 2 to 5

Answer 1

`S_4=50`

Explanation:

Sum Of Arithmetic Sequence

Given an arithmetic sequence

`a_1,\ a_1+r,\ a_1+2r,....,\ a_1+(n-1)r`

The sum of the n first terms is

`\displaystyle S_n=((a_1+a_n)n)/(2)`

Or equivalently

`\displaystyle S_n=([2a_1+(n-1)r]n)/(2)`

The given sequence is

5, 8, 11 ...

We can see the common difference between terms is r=3

We are asked to find the sum of the terms 2 to 5, it means that

`a_1=8, n=4, r=3`

`\displaystyle S_4=([2(8)+(4-1)3]4)/(2)`

`\displaystyle S_4=(100)/(2)`

`\boxed{S_4=50}`