Given the first term and the common ratio of a geometric sequence find the explicit formula.

31.) a1 = -1, r = -2
(1 is a lowered power to a)

33.) a1 = 4, r = -4
(1 is a lowered power to a)

A geometric sequence is generated by multiplying the first term in the sequence, , several times by a fixed scalar . So

and so on, down to

Using the result above, the sequences you're interested in are

31)

33)

We can rewrite these results to make them slightly cleaner.