Question

I need help with this question someone please help and explain. Find the sum of the first twenty-seven terms of an arithmetic series whose first term is -8 and the sum of the first seven-term is 28.

Answer 1

The sum of the first twenty-seven terms is 1,188

Explanation:

we know that

The formula of the sum in arithmetic sequence is equal to

`S=(n)/(2)[2a1+(n-1)d]`

where

n is the number of terms

a1 is the first term

d is the common difference (constant)

step 1

Find the common difference d

we have

n=7

a1=-8

S=28

substitute and solve for d

`28=(7)/(2)[2(-8)+(7-1)d]`

`28=(7)/(2)[-16+(6)d]`

`8=[-16+(6)d]`

`8+16=(6)d`

`d=24/(6)=4`

step 2

Find the sum of the first twenty-seven terms

we have

n=27

a1=-8

d=4

substitute

`S=(27)/(2)[2(-8)+(27-1)(4)]`

`S=(27)/(2)[(-16)+(104)]`

`S=(27)/(2)88]`

`S=1,188`