The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression.

Solution (By Examveda Team)

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
$$\eqalign{ & \Rightarrow {S_{11}} = \frac{{11}}{2}\left[ {2a + 10d} \right] \cr & \Rightarrow {S_{11}} = \frac{{11}}{2} \times 8 \cr & \Rightarrow {S_{11}} = 44 \cr} $$