**Question:**

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

**Solution:**

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 $126 .$