Question

The first term of an A.P. is $5$, the last term is $45$ and the sum of its terms is $1000$. Find the number of terms and the common difference of the A.P.

Answer 1

$\Rightarrow$$a=5$

$\Rightarrow$$a+(n-1)d=45$

$\Rightarrow$$(n-1)d=40$

$\Rightarrow$$\frac{n}{2}(2a+(n-1\left)d\right)=1000$

$\Rightarrow$$\frac{n}{2}(10+40)=1000$

$\Rightarrow$$n=40$

$\Rightarrow$$d=\frac{40}{39}$

Number of terms$=40$

Common difference$=\frac{40}{39}$