What is the sum of the first 11 terms of an arithmetic progression if the 3rd term is -1 and the 8th term is 19?
A. 204
B. 121
C. 225
D. 104
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {T_3} = a + 2d = - 1.....\,\left( 1 \right) \cr & {T_8} = a + 7d = 19\,.....\,\left( 2 \right) \cr & {\text{on solving}}\left( 1 \right)\,{\text{and}}\,\left( 2 \right) \cr & d = 4\,\& \,a = - 9 \cr & {S_n} = \frac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right] \cr} $$$${S_{11}} = \frac{{11}}{2}$$ $$\left[ {2\left( { - 9} \right) + \left( {11 - 1} \right)\left( 4 \right)} \right]$$
$$\eqalign{ & {S_{11}} = \frac{{11}}{2}\left[ {\left( { - 18} \right) + \left( {40} \right)} \right] \cr & {S_{11}} = \frac{{11}}{2}\left[ {22} \right] \cr & {S_{11}} = 121 \cr} $$
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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