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

If you look carefully you'll see that the common ratio here is - 4.

-2 times - 4 is + 8;

8 times - 4 is - 32; and so on.

A formula for this sequence would then be a (n) = a (1) * (-4) ^ (n-1), where a (1) = - 2 is the first term.

Does this "work?" Let's see if this formula produces the second term, 8:

a (2) = - 2 (-4) ^ (2-1) = - 2 (-4) = + 8. YES.

a (4) = - 2 (-4) ^ (4-1) = - 2 (-4) ^3 = - 2 (-64) = + 128. YES

A formula for this sequence would then be a (n) = a (1) * (-4) ^ (n-1)