Question

What is the common difference of an A.P. in which

$a_{21}-a_7=84$ ?

Answer 1

Given,

$a_{21}-a_7=84$

$\Rightarrow (a+20d)-(a+6d)=84$

$\Rightarrow a+20d-a-6d=84$

$\Rightarrow 20d-6d=84$

$\Rightarrow 14d=84$

$\Rightarrow d=\frac{84}{14}=6$

Hence common difference = 6