Question

Find the ${20}^{th}$ term of the AP whose $7^{th}$ term is 24 less than the ${11}^{th}$ term, first term being 12.

Answer 1

From the question, it is given that,

First-term $a=12$

$7$th term is $24$ less than the $11$th term $=T_{11}-T_7=24$

$\begin{array}{c}{T}_{11}-T_7=(a+10d)-(a+6d)=24\\ 24=a+10d-a-6d\\ 24=4d\\ d=24/4\\ d=6\end{array}$

$Now,T_{20}=a+19d$

Substitute the values of $a$ and $d$

$\begin{array}{c}{T}_{20}=12+19\left(6\right)\\ T_{20}=12+114\\ T_{20}=126\end{array}$