Question

The sum of $5$th and $9$th terms of an A.P is $72$ and the sum of $7$th and $12$th terms is $97$. Find the A.P.

• A. $6,11,16,21,........$
• B. $6,10,14,18,........$
• C. $1,6,11,16,21,........$
• D. $6,16,26,........$

Answer 1

The correct option is A $6,11,16,21,........$

Sum of $5^{th}$ and $9^{th}$ term in A.P $=72$

$(a+4d)+(a+8d)=722a+12d=72a+6d=36$

Sum of $7^{th}$ and ${12}^{th}$ term in A.P$=97$

$(a+6d)+(a+11d)=97$

$a+11d=61(\because a+6d=36)$

$5d=25d=5a=6$

A.P is $6,11,16,21,26,....$