Question

If $n$ arithmetic means are inserted between 2 and 38, then the sum of the resulting series obtained as 200. The value of $n$ is

• A. $6$
• B. $8$
• C. $9$
• D. $10$

Answer 1

Answer: (B)

$8$

There will be in total $n+2$ terms with the first term is 2 and last term as 38.

Hence

$S=\frac{n+2}{2}(a_1+a_n)$

$S=\frac{n+2}{2}(2+38)$

$200=\frac{n+2}{2}\left(40\right)$

$200=(n+2)\left(20\right)$

$n+2=10$

$n=8$.