Question

After inserting $n$ A.M.'s between 2 and 38, the sum of the resulting progression is 200. The value of $n$ is.

• A. 10
• B. 8
• C. 9
• D. None of these

Answer 1

Answer: (B)

8

Answer 2

The resulting progression will have $n + 2$ terms with 2 as the first term and 38 as the last term.

Therefore the sum of the progression

$= \frac { n + 2 } { 2 } ( 2 + 38 ) = 20 ( n + 2 )$.

By hypothesis, $20 ( n + 2 ) = 200$ $\Rightarrow$ $n = 8$.