What is the common difference of an A.P. in which a_ 21 -a_7=84 ? - Vidyadip

Question

What is the common difference of an $A.P.$ in which $a_{21}-a_7=84$ ?

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Answer

Let be the first term $d$ be the common difference of Arithmetic progression.
As,
$a_n=a+(n-1) d$
$\therefore a_{21}=a+(21-1) d=a+20 d$
$a_7=a+(7-1) d=a+6 d$
Given $a_{21}-a_7=84$
$\Rightarrow(a+20 d)-(a+6 d)=84$
$\Rightarrow a+20 d-a-6 d=84 $
$\Rightarrow 20 d-6 d=84$
$\Rightarrow 14 d=84$
Dividing both sides by $14$
$\Rightarrow \frac{14 d}{14}=\frac{84}{14} $
$\Rightarrow d=6$
Therefore, the common difference of $A.P.$ is $6$

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