Question

In an A.P. the first term is $-5$ and last term is $45$. If sum of all numbers in the A.P. is $120$, then how many terms are there? What is the common difference?

Answer 1

$a=-5$

$l=45$

$a_n=$ $l=a+(n-1)d,45=-5(n-1)d,50=(n-1)d.$

$S_2=\frac{n}{2}[2a+(n-1\left)d\right]$

$-14=\frac{n}{2}[2a+(n-1\left)2\right]$

$120=\frac{n}{2}[-10+50]$

$120=\frac{n}{2}\left[40\right]$

$120=20n$

$n=6$

$50=(n-1)d$

$50=50d$

$d=10$