Question

An AP consists of 21 terms. The sum of the three terms in the middle is 63 and sum of least three terms is 90. Find the AP.

Answer 1

The 3 middle terms are ${10}^{th},{11}^{th},\&{12}^{th}$

According to question

$T_{10}+T_{11}+T_{12}=63$

$\Rightarrow a+9d+a+10d+a+11d=63$

$\Rightarrow 3a+30d=63$

$\Rightarrow a+10d=21$.... (1)

Now,

$T_{19}+T_{20}+T_{21}=90$

$\Rightarrow a+18d+a+19d+a+20d=90$

$\Rightarrow 3a+57d=90$

$\Rightarrow a+19d=30$ .... (2)

On subtracting equation 1 from 2, we get

$9d=9$

$d=1$

$a=1$

Required A is $11,12,13,$ .... upto 21 terms