Answer
The first five terms of the geometric sequence are 6, 18, 54, 162, 486. The common ratio is 3. $a_{n} = 6(3)^{n-1}$
Work Step by Step
$a_{n} = 2(3)^{n}$ is the formula we are given for the nth term of this geometric sequence. To find the first 5 terms, plug in n =1 ,2, 3... and solve. Since the resulting terms (6,18,54,162,486) are each multiplied by a common number (the common ratio) which equals 3 in this case the sequence is geometric. To express the nth term of the sequence in standard form $a_{n} = a(r)^{n-1}$ replace a with the first term and r with the common ratio: $a_{n} = 6(3)^{n-1}$
