Arithmetic progression. find p.

AI Thread Summary
John's father loaned him $1,080 to buy a car, to be repaid in 12 monthly installments starting with an initial payment of $p, which is determined to be $570. The payments increase by $60 each month, leading to a total repayment structure that must equal the loan amount. The nth term formula for arithmetic progression (AP) is applied to find the remaining debt after n installments. There is a discussion about the accuracy of the figures, with clarification that the total loan amount is indeed $1,080, not $10,800. The conversation emphasizes the need to correctly apply the formulas for calculating the remaining debt after each installment.
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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