Question

Find the common difference of an $A.P.$ in which $a_{18}-a_{14}=32.$

• A. $8$
• B. $-8$
• C. $-4$
• D. $4$

Answer 1

The correct option is A $8$

Let the common difference of an A.P. be $d$.
Then,
$a_{18}=a_1+17\times d$
$a_{14}=a_1+13\times d$
Solving the two equations,
$a_{18}-a_{14}=a_1+17d-a_1-13d$
$\Rightarrow a_{18}-a_{14}=4d$
Substituting $4d=32$,
$\Rightarrow d=8$