Find the $14^{th}$ term of the following geometric sequence.
$3, 6, 12, 24, \dots$

Answer

Expert–verified

Hide Steps

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 $n^{t h}$ term of a geometric sequence: $a_{n} = a_{1} r^{n - 1}$

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