+0

# Geometric Series and Applications

-1
107
2
+23

What is the sum of the first 7 terms of the series −8+16−32+64−...?

Oct 14, 2021

#1
+6
+3

Add -8, 16, -32, 64, -128, 256, and -512

(-8)+16+(-32)+64+(-128)+256+(-512)=-344

Oct 14, 2021
edited by Bliss  Oct 14, 2021
edited by Bliss  Oct 14, 2021
#2
+115824
+1

thanks Bliss, that is a nice straight forward way to approach the problem.

Here is a different way

This is a GP  (Geometric progression)

the first term is -8

the common ratio r= 16/-8 = -2

$$S_n=\frac{a(r^n-1)}{r-1}\\~\\ S_7=\frac{-8((-2)^7-1)}{-2-1}\\~\\ S_7=\frac{-8(-128-1)}{-3}\\~\\ S_7=\frac{-8(-129)}{-3}\\~\\ S_7=\frac{-8(43)}{1}\\~\\ S_7=-344\\~\\$$

Oct 14, 2021