Question

Write the explicit formula that represents the geometric sequence -2, 8, -32, 128

Answer 1

first identify the first term:
this is -2
now identify your ratio (just a little more work):
divide term by previous term

Answer 2

That is take any term and its very previous term and divide that term by its previous term

Answer 3

for example any of these will give your the common ratio:
8/-2
-32/8
128/-32
that is if this is indeed a geometric sequence which the instructions have identified it as one so all of those will be spit out the same number which is....

Answer 4

-4

Answer 5

Now just put everything in
\[a_n=\text{ first term} \cdot \text{ (common ratio)} ^{n-1}\]

Answer 6

a=-2(-4)^n-1?

Answer 7

yes the whole n-1 should be a part of the superscript though
like this:
a_n=-2(-4)^(n-1)
or if I type in pretty latex:
\[a_n=-2(-4)^{n-1}\]

Answer 8

thanks