A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Tom has taken out a loan for college. He started paying off the loan with a first payment of $200. Each month he pays, he wants to pay back 1.2 times as the amount he paid the month before. Explain to Tom how to represent his first 30 payments in sigma notation. Then explain how to find the sum of his first 30 payments, using complete sentences. Explain why this series is convergent or divergent
anonymous
 one year ago
Tom has taken out a loan for college. He started paying off the loan with a first payment of $200. Each month he pays, he wants to pay back 1.2 times as the amount he paid the month before. Explain to Tom how to represent his first 30 payments in sigma notation. Then explain how to find the sum of his first 30 payments, using complete sentences. Explain why this series is convergent or divergent

This Question is Closed

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0hint: this is a geometric sequence with a = 200 being the first term r = 1.2 being the common ratio

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What was the formula for a geometric sequence again? I'm doing a lot of essay questions that need to be done in 20 minutes lol

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0The nth term of a geometric sequence is \[\Large a(r)^{n1}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And n would be the number of payments correct?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0n is the nth payment so say n = 3, that would represent the 3rd payment. To find the actual 3rd payment, plug n = 3 into the nth term expression I wrote above

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0a = 200 r = 1.2 those two values above are going to stay fixed like that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay so it would be \[200(1.2)^{31}=344.6\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0you should get this \[\Large 200(1.2)^{31}=288\] so that means payment n = 3 is $288

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0the other values of n are calculated in a similar way

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0My calculator sucks haha. I got it now. If we substitute 4 for 3 we'd get \[200(1.2)^{41}=414.72?\] or am I doing it wrong?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0it's incorrect

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0the "41" turns into "3"

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0if you are typing into a calculator, make sure to use parenthesis 200*(1.2)^(41)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0so imagine this happening all the way from n = 1 to n = 30 we could write out every single term, but that's very tedious and not necessary with proper math notation we can use sigma notation to represent a shortcut which essentially says "add up a bunch of these terms" dw:1433563109879:dw that funky looking E is the capital greek letter sigma

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0it means "add up a bunch of terms" dw:1433563144808:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433563185734:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433563205308:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0The expression \[\Large 200(1.2)^{k1}\] will go to the left of the sigma dw:1433563248671:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0so the whole drawing of this dw:1433563286174:dw means "add up 30 copies of 200*(1.2)^(k1)" where k will vary from k = 1 all the way up to k = 30
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.