Question

The first and last term of an $AP$ are $8$ and $65$ respectively. If the sum of all its terms in $730,$ find its common difference.

Answer 1

Given $730=\frac{n}{2}(a+l)$

$l=65$

$a=8$

$730=\frac{n}{2}(8+65)$

$730=\frac{n}{2}\left(73\right)$

$10=\frac{n}{2}$

$20=n$

Now $65=l=a+(n-1)d$

$65=8+(20-1)d$

$65-8=19d$

$57=19d$

$d=\frac{57}{19}=3$

The common difference is 3.