Question

If the 2^nd term of an A.P, is 13 and 5^th term is 25, what is its 7^th term?
(a) 30
(b) 33
(c) 37
(d) 38

Answer 1

Given:
2^nd term = a₂ = 13
5^th term = a₅ = 25

Now,
$$\begin{gathered} a_n=a+\left(n-1\right)d \\ {a}_2=a+\left(2-1\right)d \\ \Rightarrow 13=a+d \\ \Rightarrow a+d=13...\left(1\right) \\ {a}_5=a+\left(5-1\right)d \\ \Rightarrow 25=a+4d \\ \Rightarrow a+4d=25...\left(2\right) \\ \mathrm{Subtracting}\left(1\right)\mathrm{from}\left(2\right),\mathrm{we}\mathrm{get} \\ 3d=12 \\ \Rightarrow d=4 \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}d\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get} \\ a=9 \\ \mathrm{Therefore},a=9\mathrm{and}d=4. \\ \mathrm{Thus}, \\ {a}_7=a+\left(7-1\right)d \\ =9+6\left(4\right) \\ =33 \end{gathered}$$

Therefore, the 7^th term is 33.

​Hence, the correct option is (b).