Question

Determine whether the sequence converges or diverges. If it converges, give the limit.

48, 8, 4/3, 2/9, ...

Answer 1

If you look at the pattern, the next number is the previous number divided by 6

Answer 2

Correct?

Answer 3

So eventually as you keep dividing by 6, the denominator will become so enormous that the numerator will be so tiny compared to the denominator.

Answer 4

one of my answer choices is, "converges; 288/5"

Answer 5

What are the other choices?

Answer 6

If you divide 288/5 you will get 57.6.

Answer 7

If you keep dividing the previous number by 6, your denominator will eventually become so big that no matter what the numerator is, the decimal answer of that fraction will becomes so small.

Answer 8

Please let me know if I am speaking a different language, I don't want to confuse you. I can add more detail.

Answer 9

no, no i understand what ur saying that's why I picked "converges; 288/5"

Answer 10

That would mean that the number would somehow me multiplied by a number instead of being divided as the pattern shows. Lets think long term. If you have 100 cookies. And I take away 5 each minute, say for 20 minutes I eat all the cookies that were for a party. What will you eventually be left with?

Answer 11

you would have none left

Answer 12

That's correct. That is because of a simple subtraction problem.

Now say if you have 100 cookies and I take away 1/3rd of your remaining cookies each minute. Say for about 20 minutes. What will be the final amount of cookies you have?