Question

If the common difference of an AP is $5$, then what is $a_{18}-a_{13}$?

• A. $5$
• B. $20$
• C. $25$
• D. $30$

Answer 1

The correct option is C

$25$

Find the required value based on given information

Given, common difference is $d=5$

We know that the $n^{th}$ term of an A.P. is given by

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

where,

$a=\mathrm{first}\mathrm{term}$

$d=\mathrm{common}\mathrm{difference}$

$a_n$ is the $n^{th}$ term

Therefore

$$\begin{gathered} a_{18}-a_{13}=a+17d-\left(a+12d\right) \\ \Rightarrow a_{18}-a_{13}=5d \\ \Rightarrow a_{18}-a_{13}=5\times 5 \\ \Rightarrow a_{18}-a_{13}=25 \end{gathered}$$

Hence, $a_{18}-a_{13}=25$,

So, the correct option is (C)