What is Sn of this geometric sequence?

Question

The sequence is: 1, -3, 5, -7...

Answer 1

Not a geometric series. Looks like an alternating series of odd numbers

n (2n-1)(-1)ⁿ⁺¹ ∑

1 1 1

2 -3 -2

3 5 3

4 -7 -4

5 9 5

: : :

So, by observation

S_n = (-1)ⁿ⁺¹n

Answer 2

S1 = 1

S2 = -3

S3 = 5

S4 = -7

S5 = 9

S6 = -11

...

SN = 2N-1 if N is odd

SN = 1-2N if N is even

combine the above two versions of SN with an alternating sign

SN= 2N-1 if odd N

SN= 1-2N = -(2N-1) if even

SN = (2N-1)(-1)^N-1

the partial sums diverge and do not reach any limit