Question

Question 8
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

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,
7th term $\left(T_7\right)$ = 11th term $\left(T_{11}\right)$ - 24
[$\because$ nth term of an AP, $T_n$ = a + (n - 1)d]
$\Rightarrow$ a + (7 - 1)d = a + (11 - 1)d - 24
$\Rightarrow$ a + 6d = a + 10d - 24
$\Rightarrow$ 24 = 4d $\Rightarrow$ d = 6
$\therefore$ ${20}^{th}$ term of AP = 12 + 19 $\times$ 6 = 126