Question

The sum of $3^{rd}and{15}^{th}$ elements of an arithmetic progression is equal to the sum of $6^{th},{11}^{th},{13}^{th}$elements of the same progression. Then which element of the series should necessarily be equal to zero?

• A. 12^th
• B. 11^th
• C. 9^th
• D. 8^th

Answer 1

The correct option is A 12^th

Soln:

The$3^{rd}$ term will be$x+2d$

The${15}^{th}$ term will be$x+14d$

From the information given in the question,

$x+2d+x+14d=x+5d+x+10d+x+12d$

Solving we get,$x+11d=0$, this is nothing but the${12}^{th}$term of the series.