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]

Question

anonymous · Answer

5, -5, 5, -5, 5

anonymous · Answer

SO its a geometric equation I need

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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)

anonymous · Answer

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

anonymous · Answer

oh ok I see now thanks:)

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

oh ok thanks...

anonymous · Answer

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

anonymous · Answer

So the answer is E

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

you're welcome