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)

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