Find the \( 14^{\text {th }} \) term of the following geometric sequence.
\[
3,6,12,24, \ldots
\]

Answer

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Answer

Find the 14th term: \(a_{14} = 3\cdot 2^{14-1} = 3\cdot 2^{13} = 24576\)

Steps

Step 1 ：First, find the common ratio of the geometric sequence: \(r = \frac{6}{3} = 2 \)

Step 2 ：Use the formula for the \(n^{th}\) term of a geometric sequence: \(a_n = a_1r^{n-1}\)

Step 3 ：Find the 14th term: \(a_{14} = 3\cdot 2^{14-1} = 3\cdot 2^{13} = 24576\)