Question

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, then find the number of terms in the AP and their sum.

• A. 32; 6973
• B. 38; 6973
• C. 32; 7114
• D. 38; 7114

Answer 1

The correct option is B

38; 6973

Given,
First term $=a=17$

Last term $=l=350$

Common difference $=d=9$

Using formula $a_n=a+(n-1)d$, we can say that

$350=17+(n-1)\left(9\right)$

$\Rightarrow 350=17+9n-9$

$\Rightarrow 342=9n$

$\Rightarrow n=\frac{342}{9}=38$

Applying formula, $S_n=\frac{n}{2}(2a+(n-1\left)d\right)$, we get

$S_{38}=\frac{38}{2}(34+(38-1\left)9\right)$

$\Rightarrow S_{38}=19(34+333)=6973$

Therefore, there are 38 terms and their sum is equal to 6973.