Problem

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

Solution

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

From Solvely APP
Source: https://solvelyapp.com/problems/25626/

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