Find the 20th term of the AP whose 7th

Let the first term, common difference and number of terms of an AP are a,d and n, respectively,             Given that, first term (a) = 12.

Now by condition

7 th term $\left(T_{7}\right)=11$ th term $\left(T_{11}\right)-24$

$\left[\because n\right.$th term of an AP, $\left.T_{n}=a+(n-1) d\right]$

$\Rightarrow \quad a+(7-1) d=a+(11-1) d-24$

$\Rightarrow \quad a+6 d=a+10 d-24$

$\Rightarrow \quad 24=4 d \Rightarrow d=6$

$\therefore \quad 20$ th term of AP, $T_{20}=a+(20-1) d$

$=12+19 \times 6=126$

Hence, the required 20 th term of an AP is $126 .$