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

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8. Sequences and Series

easy

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

Solution

(b) 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$.

Standard 11

Mathematics

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