Arithmetic progression. find p.

In summary: 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
  • #1
tesha
4
0

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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  • #2
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.
 
  • #3
I suspect the total price was to be $10800, not $1080.
 
  • #4
yes it is $10800
 
  • #5
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?
 

FAQ: Arithmetic progression. find p.

What is arithmetic progression?

Arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is known as the common difference, denoted by 'd'.

How do you find the common difference in an arithmetic progression?

The common difference in an arithmetic progression can be found by subtracting any two consecutive terms in the sequence. For example, if the first term is 'a' and the second term is 'b', then the common difference is given by d = b - a.

Can you find any term in an arithmetic progression using a formula?

Yes, the general formula to find the 'n'th term in an arithmetic progression is given by: an = a + (n-1) * d, where 'a' is the first term and 'd' is the common difference.

What is the sum of an arithmetic progression?

The sum of an arithmetic progression is given by the formula: Sn = (n/2) * (2a + (n-1) * d), where 'a' is the first term, 'd' is the common difference, and 'n' is the number of terms in the sequence.

How can you find the common difference if the first and last term of an arithmetic progression are given?

The common difference can be found by using the formula: d = (an - a) / (n-1), where 'a' is the first term, 'an' is the last term, and 'n' is the number of terms in the sequence.

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