Question

Two A.P's have the same common difference. The first term of these is $3$, and that of the other is $8$. What is the difference between their
(i) $2^{nd}$ (ii) $4^{th}$ (iii) ${10}^{th}$ (iv) ${30}^{th}$ terms respectively

Answer 1

Let the common difference of the two A.P's be $d$. Then, their $n^{th}$ terms are
$a_n=3+(n-1)d$ and $b_n=8+(n-1)d$ ........$t_n=a+(n-1)d$

$⟹a_n-b_n=[3+(n-1\left)d\right]-[8+(n-1\left)d\right]$

$⟹a_n-b_n=-5$ for all $n\in N$.

Hence, $a_2-b_2=-5,a_4-b_4=-5,a_{10}-b_{10}=-5$ and $a_{30}-b_{30}=-5$.