JAMB 1991 · UME · Q28

What is the $n$ th term of the progression $27, 9, 3, \dots$ ?

Worked solution (try it first)

Each term is a third of the one before: $9 \div 27 = \frac13$ and $3 \div 9 = \frac13$ .
So this is a G.P. with $a = 27$ and $r = \frac13$ .
The $n$ th term of a G.P. is $ar^{n - 1}$ .
So the $n$ th term is $27\left(\frac13\right)^{n - 1}$ , option A.