Question 1204427
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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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<pre>
In this sequence of 10 terms, the in-pair sums of the numbers, equally remoted from the endpoints,
are a constant value:  

    {{{a[1]+a[10]}}} = {{{a[2]+a[9]}}} = {{{a[3]+a[8]}}} = {{{a[4]+a[7]}}} = {{{a[5]+a[6]}}}.


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


So, about the pair {{{a[5]+a[6]}}} we know that

    {{{a[5]+a[6]}}} = 200

    {{{a[5]-a[6]}}} =   8


From it, it is easy to guess/(to derive) that  {{{a[5]}}} = 100 + 8/2 = 104.


Now, the term {{{a[4]}}}, {{{a[3]}}}, {{{a[2]}}},  {{{a[1]}}} are

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


Thus, the first term (= the first installment) is 136.    <U>ANSWER</U>
</pre>

Solved / mentally.