Question

which term of gp 1÷3,1÷9,1÷21....... is 1÷2187

Answer 1

Correction: Third term is 1÷27, not 1÷21.
Given first term, a = 1/3; common ratio, r = (1÷9)/(1÷3) = 1/3.
Let 1÷2187 be the nth term.
$i.e. \: a \times {r}^{n - 1} = 2187 \\ \frac{1}{3} \times {( \frac{1}{3} })^{n - 1} = 2187 \\ i.e. {( \frac{1}{3} })^{n} = {( \frac{1}{3} })^{7}$
Thus n = 7