Question

If first term of an $AP$ is $5$, last term is $45$ and the sum of the terms is $400$, then the number of terms is

• A. $8$
• B. $10$
• C. $16$
• D. $20$

Answer 1

The correct option is C $16$

As we know that sum of an A.P. is given as-

$S_n=\frac{n}{2}(a+l)$

Where $a$ and $l$ are first term and last term respectively.

Given:-

$S_n=400$

$a=5$

$l=45$

$n=?$

Therefore,

$400=\frac{n}{2}(5+45)$

$400\times 2=n\times 50$

$\Rightarrow n=\frac{800}{50}=16$