Question

If the $7^{th}$ and ${13}^{th}$ terms of an AP are 34 and 64 respectively, then its ${18}^{th}$ term would be ____

• A. 87
• B. 88
• C. 89
• D. 90

Answer 1

The correct option is C 89

The $7^{th}$ term of the A.P is
$a+6d=34---\left(1\right)$

The ${13}^{th}$ term of the A.P is
$a+12d=64---\left(2\right)\text{Solving}\left(2\right)-\left(1\right),a+12d-a-6d=64-346d=30⟹d=5\text{Substituting}din\left(1\right)a+6\left(5\right)=34⟹a=4\therefore a_{18}=4+\left(17\right)5=89$