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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