Question

Is the sequence geometric? if so what is the common ratio/answers 2,-4,-16,-36/

Answer 1

We conclude that the sequence 2, -4, -16, -36,... is not a geometric sequence.

Explanation:

Given the sequence

2, -4, -16, -36,...

• A geometric sequence has a constant ratio 'r'.

Let us compute the ratio of all the adjacent terms

`(-4)/(2)=-2,\:\quad (-16)/(-4)=4,\:\quad (-36)/(-16)=2.25`

It is clear that the ratio is not constant.

Thus, the given sequence is not a geometric sequence.

Therefore, we conclude that the sequence 2, -4, -16, -36,... is not a geometric sequence.