Question

If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
(a) 87
(b) 88
(c) 89
(d) 90

Answer 1

(c) 89

$$\begin{gathered} a_7=34 \\ \Rightarrow a+6d=34.....\left(1\right) \\ \mathrm{Also},a_{13}=64 \\ \Rightarrow a+12d=64.....\left(2\right) \end{gathered}$$

Solving equations $\left(1\right)\mathrm{and}\left(2\right)$, we get:

a = 4 and d = 5

$$\begin{gathered} \therefore a_{18}=a+17d \\ =4+17\left(5\right) \\ =89 \end{gathered}$$