The fourth term of an exponential sequence is 192 and its ninth term is 6. Find the common ratio of the sequence.
-
A.
(frac{1}{3}) -
B.
(frac{1}{2}) -
C.
(2) -
D.
(3)
Correct Answer: Option B
Explanation
(T_{n} = ar^{n – 1})
(T_{4} = ar^{4 – 1} = ar^{3} = 192)
(T_{9} = ar^{9 – 1} = ar^{8} = 6)
Dividing (T_{9}) by (T_{4}),
(r^{8 – 3} = frac{6}{192})
(r^{5} = frac{1}{32} = (frac{1}{2})^{5})
(r = frac{1}{2})