The first term of a Geometric Progression (GP) is (frac{3}{4}), If the product of the second and third terms of the sequence is 972, find its common ratio.
-
A.
3 -
B.
4 -
C.
6 -
D.
12
Correct Answer: Option D
Explanation
Recall, the terms of a GP is given by (T_{n} = ar^{n – 1})
Given, (T_{1} = a = frac{3}{4}) and (T_{2} times T_{3} = ar times ar^{2} = 972)
(implies frac{3}{4}r times frac{3}{4}r^{2} = frac{9}{16}r^{3} = 972)
(r^{3} = frac{972 times 16}{9} = 1728 implies r = sqrt[3]{1728} = 12)