Question

If the $7^{\text{th}}$ and ${13}^{\text{th}}$ terms of an AP are 34 and 64, then its ${18}^{\text{th}}$ term is ___.

• A. 87
• B. 88
• C. 89
• D. 90

Answer 1

The correct option is C 89

The $n^{\text{th}}$ term of an AP of first term $a$ and common difference $d$ is
$a_n=a+(n-1)d.\Rightarrow a_7=a+6d=34---\left(1\right)a_{13}=a+12d=64---\left(2\right)\left(2\right)-\left(1\right)\Rightarrow 6d=30\Rightarrow d=5\text{Substituting d = 5 in (1), we get}a=4.\therefore a_{18}=a+17d=4+\left(17\right)5=89$