Question

What is the common difference of an A.P., in which $a_{21}-a_7=644$.

Answer 1

We know that,

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

Now, by using the above defination,

$\begin{array}{cc}{a}_{21}-a_7& =644\\ a+\left(21-1\right)d-\left[a+\left(7-1\right)d\right]& =644\\ a+20d-a-6d& =644\\ 14d& =644\\ d& =46\end{array}$

So, the difference of A.P is $46.$