If the $n$th terms of the two $APs$: $9, 7, 5, \ldots$ and $24, 21, 18, \ldots$ are the same,find the value of $n$. Also,find that term.

(N/A) For the first $AP$: $9, 7, 5, \ldots$
First term $a_1 = 9$,common difference $d_1 = 7 - 9 = -2$.
The $n$th term is $T_n = a_1 + (n - 1)d_1 = 9 + (n - 1)(-2) = 9 - 2n + 2 = 11 - 2n$.
For the second $AP$: $24, 21, 18, \ldots$
First term $a_2 = 24$,common difference $d_2 = 21 - 24 = -3$.
The $n$th term is $T_n = a_2 + (n - 1)d_2 = 24 + (n - 1)(-3) = 24 - 3n + 3 = 27 - 3n$.
Given that the $n$th terms are equal:
$11 - 2n = 27 - 3n$
$3n - 2n = 27 - 11$
$n = 16$.
Substituting $n = 16$ into either expression for the $n$th term:
$T_{16} = 11 - 2(16) = 11 - 32 = -21$.
Thus,the value of $n$ is $16$ and the term is $-21$.