Write out the first five terms of the sequence an=(−2)n. Determine if the sequence is arithmetic or geometric, and then find the common ratio or difference. Which option below is accurate?
The first five terms of the sequence are:
a1 = (-2)^1 = -2
a2 = (-2)^2 = 4
a3 = (-2)^3 = -8
a4 = (-2)^4 = 16
a5 = (-2)^5 = -32
To determine if the sequence is arithmetic or geometric, we need to check if the ratio between consecutive terms is constant. In this case, we have:
a2/a1 = 4/(-2) = -2
a3/a2 = -8/4 = -2
a4/a3 = 16/(-8) = -2
a5/a4 = -32/16 = -2
Since the ratio between consecutive terms is constant (-2), the sequence is geometric. The common ratio is -2.
Therefore, the accurate option is: The sequence is geometric, and the common ratio is -2.