Question

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

Answer 1

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

Answer 2

Lets Get started :)

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

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

Sn =
`(a1(r^n - 1))/(r -1)`
a₁ = first term of sequence = -8
r = common ration = -2
n = term of sum we need to find = 7

Sn =
`(-8((-2)^7 - 1))/(-2-1)`
= -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