Find the 7th term of the geometric sequence a3 = 128, r=-1/4

Step-by-step explanation:

The general formula for this sequence is a (n) = a (1) * (-1/4) ^ (n - 1). We don't yet know a (1).

If a (3) = 128, then 128 = a (1) * (-1/4) ^ (3 - 1), or

128 = a (1) * (1/16)

and so a (1) = 128/16

resulting in the specific formua a (n) = 8 (-1/4) ^ (n - 1)

Now let's find a (7):

a (7) = 8 (-1/4) ^1 * (-1/4) ^ (6)

or

a (7) = 8 (-1/4) ^7