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