The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression.
A)44
B)22
C)19
D)none of the above

Question

Quizplus · Accepted Answer

The sum of the third and ninth terms of an A.P. is given by $a_3 + a_9 = 2a + 2d + 8d = 2a + 10d = 8$, where $a$ is the first term and $d$ is the common difference. The sum of the first 11 terms of an A.P. is given by $S_{11} = \frac{11}{2}[2a + 10d]$. Since $2a + 10d = 8$, substituting this into the formula for $S_{11}$ gives $S_{11} = \frac{11}{2} \times 8 = 44$.

The Sum of Third and Ninth Term of an A Is