Class 11

Math

Algebra

Sequences and series

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

- $7$
- $8$
- $9$
- $10$

And the first term is $2$ and the last term is $38$

We know that,

$S_{n}=2n (a+ℓ)$

Here, $n=N+2,a=2,ℓ=38$ and $S_{N+2}=200$

$∴S_{N+2}=2N+2 (2+38)$

$⇒200=2N+2 (2+38)$

$400=40(N+2)$

$⇒10=(N+2)$

$N=8$