Question

What is the sum of a 7-term geometric series if the first term is −6, the last term is −24,576, and the common ratio is −4?

Answer 1

Do you know the formula?

Answer 2

nope...

Answer 3

@Deadly_Roses

Answer 4

The formula for the sum of a geo series is:\[S _{n}=\frac{ a _{1} (1-r^n)}{ 1-r }\]

Answer 5

would it be -34,766?

Answer 6

That's not what I got.
n=7
r=-4

Answer 7

So\[S _{n}=-6(1-(-4)^7/1-(-4)\]

Answer 8

is the fraction bar localized to 14^7/1, or does it encompass everything in parenthesis?

Answer 9

everything

Answer 10

im fried...

Answer 11

Alright.\[S _{n}=\frac{ -6(1-(-4)^7) }{ 1-(-4)}\]
This further simplifies to\[S_{n}=\frac{ -6(1-(-16834)) }{ 5 }\]
Simplify again...\[S_{n}=\frac{ -6(1+16834) }{ 5 }\]\[S_{n}=\frac{ -98310 }{ 5 }\]\[S_{n}=-19662\]

Answer 12

mind blown 0.0

Answer 13

Haha. As long as you know the series formulas, you should be good to go for any type of these problems.

Answer 14

alright. im gonna leave this open so i can write down the formula when i come back on Wednesday. thank you for your time and help

Answer 15

No problem.