Question

The first term of an AP is 5, the last term is 50 and the sum is 440. Find the number of terms and the common difference.

• A. 16; 3
• B. 17; 2
• C. 16; 2
• D. 17; 3

Answer 1

The correct option is A

16; 3

First term, $a=5$

Last term, $l=50$

$S_n=440$

Applying formula, $S_n=\frac{n}{2}(a+l)$ to find sum of n terms of AP, we get

$440=\frac{n}{2}(5+50)$

$\Rightarrow \frac{440}{55}=\frac{n}{2}$

$\Rightarrow 8=\frac{n}{2}$

$\Rightarrow n=16$

Applying formula, $S_n=\frac{n}{2}(2a+(n-1\left)d\right)$ to find sum of $n$ terms of AP and putting value of $n$, we get

$440=\frac{16}{2}\left(2\right(5)+(16-1\left)d\right)$
$\Rightarrow 440=8(10+15d)$
$\Rightarrow 10+15d=55$
$\Rightarrow 15d=45$
$\Rightarrow d=\frac{45}{15}=3$