Question

Help with one math problem! Huge challenge

Answer 1

Your friends will help you pay your new house for a while. They will give you 300 the first week, and every week after that you will receive 45% of the previous week's amount. When one week's amount drops below 1$, the payments stop. What week is the first one you will receive no payment? How much money will you receive in all? Use a formula for the nth partial sum of a geometric sequence
I will give best answer to the first correct one

Answer 2

@mathmale @Mr.ClayLordMath

Answer 3

First off, I have misgivings about your willingness to give out a reward for "the first correct (answer)." whether or not you meant it this way, it sounds as though you hope others will do the work and give you their answers to judge/check. If you've read the OpenStudy Code of Conduct, you know that's not allowed.

In this problem we have a geometric sequence (not a geometric series). Having forgotten the formula for "nth term of a geometric sequence" (if I ever knew it at all), I did an internet search for that. This is what you should be doing to obtain the correct formula.

Please see Geometric sequence nth term formula (which I obtained from

http://home.windstream.net/okrebs/page131.html:


tn = t1 . r(n - 1), where:
tn is the nth term, t1 is the first term, and r is the common ratio.

What is the value of t1, the first term, in the given sequence?
What is the common ratio, r, in the given sequence?

what you're doing is trying to find the smallest n that would satisfy

\[$1< (first.term)*(common.ratio)^{n-1}\]

Please try to find n.

If you absolutely have to, calculate the 2nd, 3rd, 4th (etc.) terms until you find the first one that's less than $1. Which n produces that term?