Question:
What is the common difference of an AP in which $a_{18}-a_{14}=32$ ?
(a) 8
(b) $-8$
(c) $-4$
(d) 4
Solution:
(a) Given, $a_{18}-a_{14}=32$
$\Rightarrow \quad a+(18-1) d-[a+(14-1) d]=32$
$\left[\because a_{n}=a+(n-1) d\right]$
$\Rightarrow \quad a+17 d-a-13 d=32$
$\Rightarrow \quad 4 d=32$
$\therefore \quad d=8$
which is the required common difference of an AP.