Question

Question 20
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 and the common difference.

Answer 1

Let the first term, common difference and the number of terms of the AP are a, d and n respectively.
Given that, first term (a) = -5 and last term (l) = 45
Sum of the terms of the $AP=120\Rightarrow S_n=120$
We know that, if last term of an AP is known, then sum of n terms of an AP is,
$S_n=\frac{n}{2}(a+l)$
$\Rightarrow 120=\frac{n}{2}(-5+45)\Rightarrow 120\times 2=40\times n$
$\Rightarrow n=3\times 2\Rightarrow n=6$
Number of terms of an AP is known, then the nth term of an AP is,
$l=a+(n-1)d\Rightarrow 45=-5+(6-1)d$
$\Rightarrow 50=5d\Rightarrow d=10$
So, the common difference is 10.