Question

An AP consists of $15$ terms. The sum of three middle most terms is $69$ and the sum of last three terms is $123$. Find the A.P.

• A. 2,5,8,11.....44
• B. 2,4,8,....62
• C. 2,3,4....16
• D. none

Answer 1

The correct option is A 2,5,8,11.....44

The $three$ middle most terms of $15$ terms is $69.$

$a_7+a_8+a_9=69$

$a_{13}+a_{14}+a_{15}=123$

$a+6d+a+7d+a+8d=69⟹3a+21d=69$....(1)

$a+12d+a+13d+a+14d=123⟹3a+39d=123$...(2)

Solving (1) and (2), we get

$18d=54\Rightarrow d=3$ and $a=2$

Thus, $2,5,8,11,\dots 44.$