SOLUTION: A man borrows 1,000 and agrees to repay with 10 instalments, each instalment being less than the preceding instalment by 8. Find the his first instalment

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Question 1204427: A man borrows 1,000 and agrees to repay with 10 instalments, each instalment being less than the preceding instalment by 8. Find the his first instalment
Answer by ikleyn(52788) About Me  (Show Source):
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A man borrows 1,000 and agrees to repay with 10 instalments, each instalment
being less than the preceding instalment by 8. Find the his first instalment
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In this sequence of 10 terms, the in-pair sums of the numbers, equally remoted from the endpoints,
are a constant value:  

    a%5B1%5D%2Ba%5B10%5D = a%5B2%5D%2Ba%5B9%5D = a%5B3%5D%2Ba%5B8%5D = a%5B4%5D%2Ba%5B7%5D = a%5B5%5D%2Ba%5B6%5D.


Therefore, each in-pair sum is  1000/5 = 200.


So, about the pair a%5B5%5D%2Ba%5B6%5D we know that

    a%5B5%5D%2Ba%5B6%5D = 200

    a%5B5%5D-a%5B6%5D =   8


From it, it is easy to guess/(to derive) that  a%5B5%5D = 100 + 8/2 = 104.


Now, the term a%5B4%5D, a%5B3%5D, a%5B2%5D,  a%5B1%5D are

    104+8 = 112,  112+8 = 120,  120+8 = 128,  128+8 = 136, respectively.


Thus, the first term (= the first installment) is 136.    ANSWER

Solved / mentally.