Question

An A.P. has $23$ terms, sum of the middle three terms is $144$, the sum of last three terms is $264$. Find the $8^{th}$ term

• A. $32$
• B. $37$
• C. $38$
• D. $28$

Answer 1

The correct option is A $32$

Given that $t_{11}+t_{12}+t_{13}=144\Rightarrow 3a+(36-3)d=144$ ...... (i)
$t_{21}+t_{22}+t_{23}=264\Rightarrow 3a+(66-3)d=264$ ......(ii)
By (ii) - (i), $d=4$ on putting in (1), $a=4$
$t_8=a+7d=4+7\times 4=32$