Question

Question 7
If the $2^{nd}$ term of an AP 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, the $2^{nd}$ term of an AP is 13.
$\Rightarrow a_2=13$
$\Rightarrow a+(2-1)d=13[\because a_n=a+(n-1\left)d\right]$
and the $5^{th}$ term of an AP is 25
$\Rightarrow a_5=25$
$\Rightarrow a+(5-1)d=25$
$\Rightarrow a+d=\mathrm{13...}\left(i\right)$
$anda+4d=25...\left(ii\right)$
On subtracting eq.(i) from eq. (ii), we get,
3d = 25 - 13 = 12
$\Rightarrow$ d = 4
From eq. (i), a = 13 - 4 = 9
$\therefore a_7=a+(7-1)d=9+6\times 4=33$