If the 3rd and 7th terms of a G.P are 9 and 1/9 respectively. Find the common ratio.

A.

\(\frac{1}{3}\)

B.

\(\frac{1}{9}\)

C.

\(\frac{2}{3}\)

D.

\(\frac{2}{9}\)

Correct answer is A

\(T_n = ar^{n - 1}\) (terms of a G.P)

\(T_3 = ar^2 = 9\) ... (i)

\(T_7 = ar^6 = \frac{1}{9}\) ... (ii)

Divide (i) by (ii);

\(\frac{ar^6}{ar^2} = \frac{\frac{1}{9}}{9}\)

\(r^4 = \frac{1}{81}\)

\(r^4 = (\frac{1}{3})^4\)

\(r = \frac{1}{3}\)