Question 1204428: A man borrows 2,00 and agrees to repay with a total interest of 340 in 12 monthly instalment, each instalment being less than the preceding instalment by 10, What should be his first instalment?
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52903)   (Show Source):
You can put this solution on YOUR website! .
A man borrows 2,00 and agrees to repay with a total interest of 340 in 12 monthly instalment, each
instalment being less than the preceding instalment by 10, What should be his first instalment?
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In order for the problem be solved correctly, it should be presented correctly.
It is a necessary preliminary requirement.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
I assume you meant to write 2,000 instead of 2,00
a = first installment = first term of arithmetic sequence
n = 12 = number of payments
d = -10 = common difference, since the payment amounts drop by 10 each time.
Sn = sum of first n terms of arithmetic sequence, aka arithmetic progression (AP)
Sn = 2000+340 = 2340 total needs to be paid back
Sn = (n/2)*(2*a + d(n-1))
2340 = (12/2)*(2*a - 10(12-1))
2340 = 6*(2a-110)
2340 = 12a-660
12a-660 = 2340
12a = 2340+660
12a = 3000
a = 3000/12
a = 250
We can use the "sequence" command in GeoGebra to generate this arithmetic progression
250, 240, 230, 220, 210, 200, 190, 180, 170, 160, 150, 140
A spreadsheet is another option.
Then add up the values and we should get to 2340
250+240+230+220+210+200+190+180+170+160+150+140 = 2340
We have confirmed the answer.
Or a shortcut
(n/2)*(1st term + 12th term) = (12/2)*(250 + 140) = 2340
Answer: 250
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