Question

If the common difference of an A.P. is 5, then a₁₈ – a₁₃ = ______________.

Answer 1

Given:
Common difference (d) = 5

Now,
$$\begin{gathered} a_n=a+\left(n-1\right)d \\ {a}_{18}=a+\left(18-1\right)d=a+17d \\ {a}_{13}=a+\left(13-1\right)d=a+12d \\ \therefore a_{18}-a_{13}=\left(a+17d\right)-\left(a+12d\right) \\ =17d-12d \\ =5d \\ =5\times 5\left(\because d=5\right) \\ =25 \end{gathered}$$

Hence, a₁₈ – a₁₃ = 25.