Question

Write the expression $a_n-a_k$ for the $A.P.a,a+b,a+2d,....$. Hence find the common difference of the $A.P.$ for which
${20}^{th}$ term is $10$ more than the ${18}^{th}$ term.

Answer 1

$a_n=a+(n-1)d$

$a_{20}-a_{18}$

$=a+19d-a-17d$

$=2d$

$\therefore 10=2d$

$\Rightarrow d=5$