If the common difference of an A.P is5, then what is ${a_{{18}^{-}}a}_{13}?$

The value of common difference is given as 5.

The nth term of an A.P is $a_n=a+(n-1)d, where 𝑎 is the first term and 𝑑is the common difference.$

The value of $a_{18}\text{ is }{a}_{18}=a+(18-1)d$

$\begin{array}{r}{a}_{18}=a+17d\\ \text{ The value of }{a}_{13}\text{ is }{a}_{13}=a+(13-1)d\\ a_{13}=a+12d\end{array}$

The difference between$a_{18}\text{ and }{a}_{13}$

$$\begin{gathered} \begin{array}{r}{a}_{18}-a_{13}=[a+17d]-[a+12d]\\ =a+17d-a-12d\\ =5d\\ =5\times 5\\ =25\end{array} \\ Therefore, the difference between a_{18} and a_{13} is 25. \end{gathered}$$