## anonymous 5 years ago Write the first five terms of the sequence defined recursively. Use the pattern to write the nth term of the sequence as a function of n. (Assume that n begins with 1.) a[1]=5,a[k+1]=-a[k]

1. anonymous

5, -5, 5, -5, 5

2. anonymous

SO its a geometric equation I need

3. anonymous

the n th term is (-1)^(n+1) * 5

4. anonymous

the sequence would be f(n) = 5*(-1)^(n+1)

5. anonymous

ok well these are my options: a[n]=5n a[n]=5(-1)^n a[n]=-5^n a[n]=-5^(n-1) a[n]=5(-1)^(n-1)

6. anonymous

the last one. (-1)^(n+1) = (-1)^(n-1)

7. anonymous

oh ok I see now thanks:)

8. anonymous

Find the sum of the infinite series. $\sum_{i=1}^{\infty}2(-1/4)^i$ A. Undefined B. -2/3 C. 2 D.4/5 E. -2/5

9. anonymous

Ratio test shows that it converges. I cannot recall how to find what it converges to however.

10. anonymous

oh ok thanks...

11. anonymous

This is a geometric series with a = -1/4 and r = -1/4, after you factor the 2 out

12. anonymous

13. anonymous

The infinite sum for a geometric series is a/(1-r) provided |r| < 1

14. anonymous

oh ok so I would just plug those in and get my answer! Thanks so much!

15. anonymous

you're welcome