The 3rd and 6th terms of a geometric progression (G.P.) are (frac{8}{3}) and (frac{64}{81}) respectively, find the common ratio.
-
A.
(frac{1}{3}) -
B.
(frac{2}{3}) -
C.
(frac{3}{4}) -
D.
(frac{4}{3})
Correct Answer: Option B
Explanation
(T_{n} = ar^{n-1}) (for a geometric progression)
(T_{3} = ar^{3-1} = ar^{2} = frac{8}{3})
(T_{6} = ar^{6-1} = ar^{5} = frac{64}{81})
Dividing (T_{6}) by (T_{3}),
(frac{ar^{5}}{ar^{2}} = frac{frac{64}{81}}{frac{8}{3}} implies r^{3} = frac{8}{27})
(therefore r = sqrt[3]{frac{8}{27}} = frac{2}{3})