SOLUTION: cost of a borehole is �400 for the first meter and increases by �25 for each successive meter, calculate the cost of the borehole if it is 24 m deep.

Question 936674: cost of a borehole is �400 for the first meter and increases by �25 for each successive meter, calculate the cost of the borehole if it is 24 m deep.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
the problem statement is not clear, so there are two possible interpretations:
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A) first interpretation:
meter 1 = 400
meter 2 = 25
meter 3 = 25
...
400 + 25*23 = 975
answer A:
borehole cost = 975
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B) second interpretation:
meter 1 = 400
meter 2 = 400+25
meter 3 = 400+25+25
...
400 + 400+(25*1) + 400+(25*2) ... + 400+(25*22) + 400+(25*23) = ???
24*400 + 25*(1+2+ ... +22+23) = ???
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the sum of consecutive integers from n to m = (m-n+1)*(n+m)/2
---
24*400 + 25*(m-n+1)*(n+m)/2 = ???
24*400 + 25*(23-1+1)*(1+23)/2 = 16500
answer B:
borehole cost = 16500
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