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: Option A
Explanation
(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})
There is an explanation video available below.