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) = 1Last term (l) = 11
and sum of its terms = 36
Let n be the number of terms and d be the common difference, then
$$\eqalign{ & {a_n} = 1 = a + \left( {n - 1} \right)d = 11 \cr & \Rightarrow 1 + \left( {n - 1} \right)d = 11 \cr & \Rightarrow \left( {n - 1} \right)d = 11 - 1 \cr & \Rightarrow \left( {n - 1} \right)d = 10\,.....\,\left( 1 \right) \cr & {S_n} = \frac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right] = 36 \cr} $$
$$ \Rightarrow \frac{n}{2}\left[ {2 \times 1 + 10} \right] = 36\,$$ $$\left[ {{\text{From}}\,\left( 1 \right)} \right]$$
$$\eqalign{ & \Rightarrow n\left( {2 + 10} \right) = 72 \cr & \Rightarrow 12n = 72 \cr & \Rightarrow n = \frac{{72}}{{12}} \cr & \Rightarrow n = 6 \cr} $$
Related Questions on Progressions
Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.
A. 5
B. 6
C. 4
D. 3
E. 7
The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
A. 600
B. 765
C. 640
D. 680
E. 690
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