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.
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.
The error you mentioned in the equation is indeed in the formula for finding the explicit formula. Let's go through the process step by step to find the error and arrive at the correct solution.
To find the explicit formula, we need to identify the pattern in the given sequence of amounts owed. The amounts are as follows: $937.50, $875.00, $812.50, $750.00, $687.00.
Looking at the given sequence, we can observe that each subsequent amount is decreasing by $62.50. So, the monthly payments must be $62.50.
Now, let's find the explicit formula using the difference between consecutive terms:
a2 - a1 = $875.00 - $937.50 = -$62.50
a3 - a2 = $812.50 - $875.00 = -$62.50
a4 - a3 = $750.00 - $812.50 = -$62.50
a5 - a4 = $687.00 - $750.00 = -$62.50
As you correctly identified, the difference is constant at -$62.50. Therefore, the explicit formula for the sequence is:
an = a1 - (n-1) * d
Now, let's evaluate the formula for n = 12:
a12 = $937.50 - (12-1) * (-$62.50)
= $937.50 - 11 * $62.50
= $937.50 - $687.50
= $250.00
So, the correct answer is that you still owe him $250.00 at the end of one year.
Correcting the error you mentioned, the explicit formula should be:
an = a1 - (n-1) * d
where a1 = $937.50, d = -$62.50
Therefore, the correct explicit formula is:
an = $937.50 - (n-1) * $62.50
To evaluate the formula for n = 12, we substitute n = 12 into the formula:
a12 = $937.50 - (12-1) * $62.50
= $937.50 - 11 * $62.50
= $937.50 - $687.50
= $250.00
So, the correct answer is that you still owe him $250.00 at the end of one year.