## anonymous 4 years ago The sum of a geometric series is -2044. If the first term is -4 and the common ratio is 2, what is the final term in the sequence?

1. anonymous

Sn = a[r^n-1]/r-1

2. anonymous

use this and find n

3. anonymous

Wait @Yahoo!

4. anonymous

then an = a*r^(n-1)

5. anonymous

Why @waterineyes any mistake

6. anonymous

Sorry my mistake... Ha ha ha..

7. anonymous

$-2044 = -4[2^n -1]/(2-1)$

8. anonymous

511 = 2^n - 1 510 = 2^n

9. anonymous

find n??

$$-2044 = -4. \frac{2^{n}-1}{2-1}$$ $$-2044 = -4. (2^{n}-1)$$ $$511 = 2^{n}-1$$ $$512 = 2^{n}$$ $$2^9 = 2^{n}$$ 9=n

11. anonymous

512

12. anonymous

sorry 512 = 2^n

13. anonymous

now n = 9

14. anonymous

subs in an = a * r^(n-1)

15. anonymous

$\large 2^n = 512 \implies 2^n = 2^9 \implies \color{green}{n = 9}$

16. anonymous

an = -4 * 2^8

17. anonymous

you can replace n here by 9 @Yahoo!

18. anonymous

256 * -4 = -1024

19. anonymous

lol thanks!

20. anonymous

Welcome