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The terms given are
- 8 , + 16 , - 32 , + 64
The formula for finding the sum of this geometric sequence is:
Sn = [tex] \frac{a1(r^n - 1)}{r -1} [/tex]
a₁ = first term of sequence = -8
r = common ration = -2
n = term of sum we need to find = 7
Sn = [tex] \frac{-8((-2)^7 - 1)}{-2-1} [/tex]
= -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
