Question

Determine whether the sequence converges or diverges. If it converges, give the limit.
60, -10, 5/3, -5/18
A. Diverges
B. Converges: 11.100
C. Converges: 72
D. Converges: 0

Answer 1

What's the common ratio, and therefore the formula for the nth term of the sequence?

Answer 2

I have no idea how to do these equations, or formulas

Answer 3

You need to spend some time going over this in your books then. The common ratio is how much it changes by each time. In this case, we can see it's dividing by -6 each time so our common ratio is -1/6 (the amount we multiply a term by to get the next term). The formula for the nth term of a geometric sequence is:
\[a_n=ar^{n-1}\]
a is the first term = 60
r is the common ratio = -1/6
n is the term we want to find
\[a_n=60*(-\frac{1}{6})^{n-1}\]

As n gets bigger, this gets closer and closer to 0. It converges to 0. Try it, sub in a huge number and see what answer you get.

Answer 4

so just plug in some random number for n?

Answer 5

well, common sense is that the terms' absolute value (magnitude) decreases.
So at certain point, the terms will become so insignificant (almost 0).

just that fact indicates that it converges or diverges?

Answer 6

diverges?

Answer 7

?