Arithmetic progression. find p.

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Homework Help Overview

The problem involves a loan of $1080 to be repaid in 12 monthly installments, starting with an initial payment of $p that increases by $60 each month. Participants are tasked with showing that p = 570 and finding an expression for the remaining debt after n installments.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of the nth term formula and the sum formula for arithmetic progressions to determine the initial payment p. There are questions about the correctness of the figures provided, particularly regarding the total loan amount.

Discussion Status

There is ongoing exploration of the problem, with some participants questioning the initial payment calculation and the total loan amount. Guidance has been offered regarding the use of specific formulas, but no consensus has been reached on the correct approach or values.

Contextual Notes

Participants have noted potential discrepancies in the loan amount, with suggestions that it may be $10800 instead of $1080, which could affect the calculations.

tesha
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Homework Statement


johns father gave him a loan of $1080 to buy a car. the loan was to repaid in 12 monthly installments starting with an intial payment of $p in the 1st month. there is no interest charged on the loan but the installments increase by $60/month. a) show that p = 570 and find in terms of n where 1 is greater than or equal to n where it is greater than or equal to 12 an expression for the remaining debt on the loan after john has made the nth instalment.

Homework Equations



the nth term of the AP. tn = a +(n-1)d. the sum formula Sn= n/2[2a+(n-1)d]

The Attempt at a Solution


I tried using the tn formula using the common difference of 60 to find p but that didn't work.
 
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tesha said:

Homework Statement


johns father gave him a loan of $1080 to buy a car. the loan was to repaid in 12 monthly installments starting with an intial payment of $p in the 1st month. there is no interest charged on the loan but the installments increase by $60/month. a) show that p = 570 and find in terms of n where 1 is greater than or equal to n where it is greater than or equal to 12 an expression for the remaining debt on the loan after john has made the nth instalment.

Homework Equations



the nth term of the AP. tn = a +(n-1)d. the sum formula Sn= n/2[2a+(n-1)d]

The Attempt at a Solution


I tried using the tn formula using the common difference of 60 to find p but that didn't work.
Are you sure these figures are correct?

If the initial payment is $570, then the loan is paid off in about 2 months, give or take.
 
I suspect the total price was to be $10800, not $1080.
 
yes it is $10800
 
tesha said:

Homework Statement


johns father gave him a loan of $1080 to buy a car. the loan was to repaid in 12 monthly installments starting with an intial payment of $p in the 1st month. there is no interest charged on the loan but the installments increase by $60/month. a) show that p = 570 and find in terms of n where 1 is greater than or equal to n where it is greater than or equal to 12 an expression for the remaining debt on the loan after john has made the nth instalment.

Homework Equations



the nth term of the AP. tn = a +(n-1)d. the sum formula Sn= n/2[2a+(n-1)d]

The Attempt at a Solution


I tried using the tn formula using the common difference of 60 to find p but that didn't work.

What does "that didn't work" mean exactly? Did you try this formula with a = $570, d = $60, and n = 12?
 

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