## anonymous one year ago 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?

1. PhantomCrow

Do you know the formula?

2. anonymous

nope...

3. anonymous

4. PhantomCrow

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

5. anonymous

would it be -34,766?

6. PhantomCrow

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

7. PhantomCrow

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

8. anonymous

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

9. PhantomCrow

everything

10. anonymous

im fried...

11. PhantomCrow

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$

12. anonymous

mind blown 0.0

13. PhantomCrow

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

14. anonymous

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

15. PhantomCrow

No problem.