Question

If the sum of $5$ terms of an $A.P.$ is same as the sum of its $11$ terms then sum of $16$ is

• A. $0$
• B. $16$
• C. $-16$
• D. $32$

Answer 1

Answer: (A)

$0$

Let $a$ and $d$ be the first term and common difference of the A.P. respectively.

Then the sum of $5$ terms in the A.P. be $\frac{5}{2}(2a+d(5-1\left)\right)=5(a+2d)$......(1).

Again the sum of $11$ terms in the A.P. be $\frac{11}{2}(2a+d(11-1\left)\right)=11(a+5d)$......(2).

By the problem

$5(a+2d)=11(a+5d)$

or, $6a+45d=0$

or, $2a+15d=0$......(3).

Now sum of $16$ terms of the A.P. be $\frac{16}{2}(2a+15d)=0$ [Using (3)]