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

-8 + 16 + -32 + 64 + -128 + 256 + -512 (These are the first 7 terms) The total = -344

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The terms given are 
- 8 , + 16 , - 32 , + 64

The formula for finding the sum of this geometric sequence is:

Sn = 
a₁ = first term of sequence = -8
r = common ration = -2
n = term of sum we need to find = 7

Sn = 
     = -344

There is also another way, by simply adding, but you cannot perform this when they ask for a larger terms sums

Each term are multiplied by - 2, so to find the rest of the terms, we multiply by - 2 

+ 64 x - 2 = - 128
- 128 x -2 = + 256
+256 x - 2 = - 512

( - 8 ) + ( 16 ) + ( - 32 ) + ( 64 ) + ( - 128 ) + ( 256 ) + ( - 512 ) (first 7 terms)
= -344

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