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

We know, the formula to find the $n^{th}$ term of A.P.,

$\Rightarrow a_n=a+(n-1)d$

Where, $a_n$ is the $n^{th} term$, $a$ is the first term of the A.P., $n$ is the total number of terms and $d$ is the common difference.

Now, first let's find $a_{18}$, in which $n=18$,

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

$\Rightarrow a_{18}=a+17d$             [equation I]

Now, first let's find $a_{14}$, in which $n=14$,

$\Rightarrow a_{14}=a+(14-1)d$

$\Rightarrow a_{14}=a+13d$            [equation II]

Now, it is given that,

$\Rightarrow a_{18}-a_{14}=32$

$\Rightarrow a+17d-\left(a+13d\right)=32$

$\Rightarrow a+17d-a-13d=32$

$\Rightarrow 4d=32$

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

$\Rightarrow d=8$