Question

Can you find the error for me in this equation, find the explicit formula, evaluate the formula for n?
I think the error is in the
a2-a1 formula.and the -62.50.
I know the pattern is 62.50 paid per month.

Your uncle loaned you some money and did not charge interest. The amount you owe him at the end of the first 5 months is $937.50, $875.00, $812.50, $750.00 and $687.00. If the pattern continues, how much will you still owe him at the end of one year?

Compare the terms in the sequence to find a pattern. Then generalize in terms of n.

a2 - a1 = 875,00 - 937.50 = -62.50
a3 - a2 = 812.50 - 875.00 = -62.50
a4 - a3 = 750.00 - 812.00 = - 62.50
a5 - a4 = 687.00 - 750.00 = -62.50

an-an-1 = -62.50

Find an explicit formula.

an = 937.5- 62.50

Evaluate the form for n = 12.
an = 937.5 -62.5n
a12 = 937.5 - 62.5(12)
= 187.5
You still owe him $187.50 at the end of one year.

Answer 1

N = $937.50
M = Month.

BAL = N - (M-1)*62.50

Balance at end of:

1st = $937.50
2nd = 875.00
3rd = 812.50
4th = 750.00
5th = 687.50.

12th = $250.00

BAL = 937.50 - (12-1)*62.50 = 250.