A camera to be sent inside the hole and the firm charges £15 for the first metre with an increase of £2 per metre for... The full question is below.

Aron Ronnie

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An investigation should happen underground to a depth of 90m. A camera to be sent inside the hole and the firm charges £15 for the first metre with an increase of £2 per metre for each succeeding metre. If another additional 25 metres has to be investigated what will be the cost of those 25 metres??
 

Subhotosh Khan

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An investigation should happen underground to a depth of 90m. A camera to be sent inside the hole and the firm charges £15 for the first metre with an increase of £2 per metre for each succeeding metre. If another additional 25 metres has to be investigated what will be the cost of those 25 metres??
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HallsofIvy

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An investigation should happen underground to a depth of 90m. A camera to be sent inside the hole and the firm charges £15 for the first metre with an increase of £2 per metre for each succeeding metre. If another additional 25 metres has to be investigated what will be the cost of those 25 metres??
So the cost for the second metre is 15+ 2= £17, for the third metre is 17+ 2= £19, etc. Then you have you have the arithmetic series 15+ 17+19+ ... 59+ 61+ 63

One way to sum that is to write it as
15+ 17+19+ ...+ 59+ 61+ 63 and reverse it
63+ 61+ 59+...+ 19+ 17+ 15 and add VERTICALLY
15+ 63= 78, 17+ 61= 78, etc. Every sum is 78 and there are 24 such sums so the sum of both sequences is 24(78)= 1872. .........edited

Of course that is adding twice, so just one sum is 1872/2= £936,
 
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