Question

The first term of an AP is $5$, last term is $45$ and the sum is $400,$ then the number of terms and common difference of the series are respectively :

• A. $12,\frac{8}{3}$
• B. $16,\frac{8}{3}$
• C. $16,\frac{6}{11}$
• D. $8,\frac{6}{11}$

Answer 1

The correct option is B $16,\frac{8}{3}$

Given,
$a=5,l=45,S_n=400$

We know that,
$S_n=\frac{n}{2}[a+l]\Rightarrow 400=\frac{n}{2}[5+45]\Rightarrow n=\frac{400}{25}\Rightarrow n=16$

and
$l=a+(n-1)d\Rightarrow 45=5+(16-1)d\Rightarrow d=\frac{40}{15}\Rightarrow d=\frac{8}{3}$