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# Choose the correct answer from the given four options:

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

**(A)** 8

**(B)** $ -8 $

**(C)** $ -4 $

**(D)** 4

Given:

\( a_{18}-a_{14}=32 \)

To do:

We have to find the common difference of the AP.

Solution:

Let the common difference be $d$

Let $a$ be the first term of the A.P.

$\therefore a_{18}=a+( 18-1)d$

$\Rightarrow a_{18}=a+17d$

Similarly, $a_{14}=a+( 14-1)d$

$\Rightarrow a_{14}=a+13d$

$\therefore a_{18}-a_{14}=a+17d-a-13d=32$

$4d=32$

$d=\frac{32}{4}$

$d=8$

The common difference of the given AP is $8$.

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