Question

Question 10
What is the common difference of an AP in which
$a_{18}-a_{14}=32?$

A) 8
B) -8
C) -4
D) 4

Answer 1

$Given,a_{18}-a_{14}=32$
$\Rightarrow a+(18-1)d-[a+(14-1\left)d\right]=32[\because a_n=a+(n-1\left)d\right]$
$\Rightarrow a+17d-a-13d=32$
$\Rightarrow 4d=32$
$\therefore d=8$
Hence, the common difference of the A.P is 8.