Question

The first term of an AP is 5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms.

Answer 1

Here $a=5$ and
last term $=a_n=a+(n-1)d=45$
$\Rightarrow a_n=5+(n-1)d=45\Rightarrow (n-1)d=40$ ...(1)
Again $S_n=\frac{n}{2}(a+a_n)$
$\Rightarrow 120=\frac{n}{2}(5+45)$
$\Rightarrow n=\frac{240}{50}$
$\Rightarrow n=4.8$, which is not possible.