Question
The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression.
Answer: Option A
The third term t3 = a + 2d
The ninth term t9 = a + 8d
t3 + t9 = 2a + 10d = 8
Sum of first 11 terms of an AP is given by
$$\eqalign{
& \Rightarrow {S_{11}} = \frac{{11}}{2}\left[ {2a + 10d} \right] \cr
& \Rightarrow {S_{11}} = \frac{{11}}{2} \times 8 \cr
& \Rightarrow {S_{11}} = 44 \cr} $$
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The third term t3 = a + 2d
The ninth term t9 = a + 8d
t3 + t9 = 2a + 10d = 8
Sum of first 11 terms of an AP is given by
$$\eqalign{
& \Rightarrow {S_{11}} = \frac{{11}}{2}\left[ {2a + 10d} \right] \cr
& \Rightarrow {S_{11}} = \frac{{11}}{2} \times 8 \cr
& \Rightarrow {S_{11}} = 44 \cr} $$
Was this answer helpful ?
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