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

Answer:

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

Step-by-step explanation:

we know that

The formula of the sum in arithmetic sequence is equal to

$S=\frac{n}{2}[2a1+(n-1)d]$

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

$28=\frac{7}{2}[2(-8)+(7-1)d]$

$28=\frac{7}{2}[-16+(6)d]$

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

$8+16=(6)d$

$d=24/(6)=4$

step 2

Find the sum of the first twenty-seven terms

we have

n=27

a1=-8

d=4

substitute

$S=\frac{27}{2}[2(-8)+(27-1)(4)]$

$S=\frac{27}{2}[(-16)+(104)]$

$S=\frac{27}{2}88]$

$S=1,188$