Question

Second term in an AP is 8 and the 8th term is 2 more than thrice the second term. Find the sum up to 8 terms of this AP

CAT 2021

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

Solution

Correct option is

(A)

Explanatory Answer :

Second term = $a_{2}=8$

a+d=8 ---1

We are given that the 8th term is 2 more than the thrice the second term

Formula of nth term = $a_{n}=a+(n-1)d$

$a_{8}=a+7d$

ATQ , a+7d=2+3(8)

a+7d=2+24

a+7d=26

Using 1

a+7(8-a)=26

a+56-7a=26

30=6a

5=a

Sum of first n terms = $s_{n}=n/2[2a+(n-1)d]$

$s_{8}=8/2[2a+7d]$

$s_{8}=4[5+26]$

$s_{8}=124$

Hence the sum of first 8 terms is 124