Question

If the common difference of an AP is 5,then what is a18 -a13 ?
5
20
30
25​

Answer 1

       $\underline{\bold{Answer:}}$

       $25$

       $\underline{\bold{Step-by-step-explaination:}}$

       $\text{The common difference of the A.P} = 5$

       $\text{We know that, the }n^{th} \text{ term of an A.P}(a_n) = a + (n-1)d \text{ where }\\a = \text{first term and }d = \text{common difference}$

       $\text{We must find }a_{18} - a_{13}$

$\implies a_{18} - a_{13} = a + (18-1)(5) - [a + (13-1)(5)]$

$\implies a_{18} - a_{13} = a + (17)(5) - [a + (12)(5)]$

$\implies a_{18} - a_{13} = a + 85 - [a + 60]$

$\implies a_{18} - a_{13} = a + 85 - a - 60$

$\implies a_{18} - a_{13} = 85 - 60$

$\implies \boxed{a_{18} - a_{13} = 25}$