## anonymous one year ago Write a formula for the general term (the nth term) of the geometric sequence. 1/2 -1/10 1/50 -1/250

1. anonymous

@phi @welshfella

2. anonymous

A. an = 1/2(n-1)3/5 B. an = 1/2 - 1/5(n-1) C. an = (1/2)(-1/5)(n-1) D. an = (1/5)(-1/2)(n-1)

3. phi

any idea how to "get" from 1/2 to -1/10 ? what do you multiply 1/2 by to get -1/10 ?

4. anonymous

5 maybe

5. phi

right track. but you can do better $\frac{1}{2} \cdot x =- \frac{1}{10}$

6. phi

if you multiply by 5 you get $\frac{5}{2}$ not what we want

7. anonymous

1/5

8. phi

if you can't see it, try multiplying both sides by 2 and "solve for x" 1/5 is pretty good, but not quite $\frac{1}{2} \cdot \frac{1}{5}= \frac{1}{10}$ but we want $- \frac{1}{10}$

9. anonymous

so -1/5

10. phi

ok, and to make sure take the 2nd term in the series -1/10 and multiply by -1/5 what do we get ?

11. anonymous

1/15

12. anonymous

i think

13. phi

multiply top times top and bottom times bottom

14. anonymous

ok so 1/50

15. phi

and if we multiply 1/50 by -1/5 we get -1/250 notice we are getting the original series 1/2 -1/10 1/50 -1/250

16. anonymous

yes

17. phi

here is what we know $\frac{1}{2} \\ \frac{1}{2}\left(-\frac{1}{5}\right)^1 \\ \frac{1}{2}\left(-\frac{1}{5}\right)^2$ and so on

18. anonymous

yes

19. phi

if we label the first term as "term number 1" and the 2nd 2 and then 3 etc notice each term has 1/2 times (-1/5) to a power one less than the term's number

20. anonymous

yes that makes sence

21. phi

only one of the choices is "short-hand" for that

22. anonymous

c

23. phi

yes

24. anonymous

yeah thnx again freind