What is the sum of the first five terms of the geometric series 3 − 6 + 12 − . . ?

3,−6,12,−24,...

You can rewrite this as:

(−1)n3⋅(1,2,4,8,...)

If we focus on 1,2,4,8...

an+1=2an
with a0=1.

This can be written out as a nice sum:
N∑n=02n=20+21+22+23+...
=1+2+4+8+...

Thus, now we can recombine everything to get:

3N∑n=0(−1)n2n

16

step-by-step explanation:

2 x 40 = 80

80/5

= 16

good job you smart son of a gun you are smarter that einstein. 7