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The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be

A. 5

B. 6

C. 7

D. 8

Answer: Option B

Solution(By Examveda Team)

First term of an A.P. (a) = 1
Last term (l) = 11
and sum of its terms = 36
Let n be the number of terms and d be the common difference, then
$$\eqalign{ & {a_n} = 1 = a + \left( {n - 1} \right)d = 11 \cr & \Rightarrow 1 + \left( {n - 1} \right)d = 11 \cr & \Rightarrow \left( {n - 1} \right)d = 11 - 1 \cr & \Rightarrow \left( {n - 1} \right)d = 10\,.....\,\left( 1 \right) \cr & {S_n} = \frac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right] = 36 \cr} $$
$$ \Rightarrow \frac{n}{2}\left[ {2 \times 1 + 10} \right] = 36\,$$       $$\left[ {{\text{From}}\,\left( 1 \right)} \right]$$
$$\eqalign{ & \Rightarrow n\left( {2 + 10} \right) = 72 \cr & \Rightarrow 12n = 72 \cr & \Rightarrow n = \frac{{72}}{{12}} \cr & \Rightarrow n = 6 \cr} $$

This Question Belongs to Arithmetic Ability >> Progressions

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