First term of first AP, a = 9

First term of second AP, A = 24

Common difference of first AP, d = 7 - 9 = - 2

Common difference of second AP, D = 21 - 24 = - 3

Given that nth term is same i.e

A_n = a_n

As we know, nth term of an AP is

a_{n =} a + (n - 1)d

where a = first term

a_n is nth term

d is the common difference

A + (n - 1)D = a + (n - 1)d

24 + (n - 1) (- 3) = 9 + (n - 1) (- 2)

24 - 3n + 3 = 9 - 2n + 2

27 - 3n = 11 - 2n

3n - 2n = 27 - 11

n = 16

i.e their 16^th term is equal in both cases,

and a₁₆ = A₁₆ = a + 15d = 9 + 15 (- 2) = - 21