Question

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]

Answer 1

5, -5, 5, -5, 5

Answer 2

SO its a geometric equation I need

Answer 3

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

Answer 4

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

Answer 5

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)

Answer 6

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

Answer 7

oh ok I see now thanks:)

Answer 8

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

Answer 9

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

Answer 10

oh ok thanks...

Answer 11

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

Answer 12

So the answer is E

Answer 13

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

Answer 14

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

Answer 15

you're welcome