If the common difference of an AP is $5$, then what is $a_{18} – a_{13}$?
Given: The common difference of an AP is $5$
To do: To find $a_{18}-a_{13}=?$
Solution:
As given, common difference $d=5$
Let $a$ be the first term of the A.P.
$\therefore a_{18}=a+( 18-1)5$
$\Rightarrow a_{18}=a+85$
Similarly, $a_{13}=a+( 13-1)5$
$\Rightarrow a_{13}=a+60$
$\therefore a_{18}-a_{13}=a+85-a-60=25$
Thus, $a_{18}-a_{13}=25$.
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