Answer
The first five terms of the sequence are -2,4,-8,16,-32. The sequence is geometric with a common ratio of -2. $a_{n} = -2(-2)^{n-1}$
Work Step by Step
$a_{n} = (-1)^{n}2^{n}$ is the formula we are given for the nth term of this sequence. To find the first 5 terms, plug in n =1 ,2, 3... and solve. Since the resulting terms (-2,4,-8,16,-32) are each multiplied by a common number (the common ratio) which equals -2 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: $a_{n} = -2(-2)^{n-1}$
