Question

-1, 6, -36, 216, …
is this an arithmetic series, geometric series, or neither?If arithmetic, state the common difference. If geometric, state the common ratio.

Answer 1

@jim_thompson5910 any chance u know about sequences and series?

Answer 2

it's a geometric series

Answer 3

the successive terms are obtained by multiplying the previous terms by -6

Answer 4

So first you assume that it is an arithmetic series. If it is true, then the difference between the terms should be the same.
6 - -1 should equal to -36 - 6.
But this isnn't true because 7 does not equal to -42

now we know that it is not an arithmetic sequence. So now let's assume it is an geometric series. then there should be a common ratio, such that

6/-1 should equal to -36/ 6 and also equal to 216/-36

clearly they equal to -6. We can safely assume that it is a geometric sequence with the common ratio of -6