Question
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?
Answers
GPT 3.5
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.
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.