Question

Find the sum of the first 11 terms of the sequence -7,-4,-1, 2 ...

[A] 88
[B] 91
[C] 85
[D] 176

Answer 1

A The sum of the first 11 terms is 88

Explanation:

Since -4 - (-7) = -1 - (-4) = 2 - (-1) = 3

Your sequence is an arithmetic sequence with a common difference of 3.

The formula for the sum of an arithmetic sequence is

`S = (n(a_(1) + a_(n)) )/(2)` where
`a_(1) = the first term, a_(n) = the last term, n = the number of terms to be added, and S = the sum`

In your case
`a_(1) = -7`, n = 11 and
`a_(n) = a_(11)`

We know everything except the eleventh term.

So, we need to find the eleventh term or
`a_(11)` =
`a_(1)` + (n - 1)d

= -7 + (11 - 1)3

= -7 + 30 = 23

Now, S =
`(11(-7 + 23))/(2) = (11(16))/(2) = 88`

The sum of the first 11 terms is 88