katiebugg 2 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. Yahoo!

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

2. Yahoo!

use this and find n

3. waterineyes

Wait @Yahoo!

4. Yahoo!

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

5. Yahoo!

Why @waterineyes any mistake

6. waterineyes

Sorry my mistake... Ha ha ha..

7. Yahoo!

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

8. Yahoo!

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

9. Yahoo!

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. waterineyes

512

12. Yahoo!

sorry 512 = 2^n

13. Yahoo!

now n = 9

14. Yahoo!

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

15. waterineyes

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

16. Yahoo!

an = -4 * 2^8

17. waterineyes

you can replace n here by 9 @Yahoo!

18. Yahoo!

256 * -4 = -1024

19. katiebugg

lol thanks!

20. Yahoo!

Welcome