What are the non recursive system generating functions

What is the non recursive system generating function for these 2 sequences:

a) -7,-3,1,5...

b)-1/32, 4/16, -7/8, 10/4, -13/2

Thanks so much! :)

a) The difference between successive terms is a constant, so this is an arithmetic sequence.

a_1 = -7, d = (-3 - (-7)) = 4

a_n = a_1 + (n - 1)d = -7 + (n - 1)4 = 4n - 11


b) The terms alternate in sign, and a_1 is negative, so we'll need a factor of (-1)^n. Now consider the absolute value of the terms.

The numerators form an arithmetic sequence with a_1 = 1 and d = 3. So the numerator of a_n is given by (1 + 3(n - 1)) = (3n - 2)

The denominators form a geometric sequence with a_1 = 32 and r = ½ So the denominator of a_n is given by 32*(½^(n-1)) = 64 * ½^n

Putting the pieces together, the expression for a_n is

a_n = (-1)^n (3n - 2) / [64 * ½^n]

which may be simplified to

a_n = (-2)^n (3n - 2)/64

or, since (-2)^6 = 64,

a_n = [(-2)^(n - 6)](3n - 2)