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
\(\frac{2}{9}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(T_n = ar^{n - 1}\) (terms of a G.P)
\(T_3 = ar^2 = 9\) ... (i)
\(T_7 = ar^6 = \frac{1}{9}\) ... (ii)
Divide (i) by (ii);
\(\frac{ar^6}{ar^2} = \frac{\frac{1}{9}}{9}\)
\(r^4 = \frac{1}{81}\)
\(r^4 = (\frac{1}{3})^4\)
\(r = \frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #55382)