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

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(52790) (Show Source): You can put this solution on YOUR website!
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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:  

     =  =  =  = .


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


So, about the pair  we know that

     = 200

     =   8


From it, it is easy to guess/(to derive) that   = 100 + 8/2 = 104.


Now, the term , , ,   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.

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