The Student Room Group

C1 question.

Can someone answer the following question, tnx.
Prospectors are drilling for oil. The cost of drilling to a depth of 50m is £500. To drill a futher 50m costs £640, and hence, the total cost of drilling to a depth of 100m is £1140. Each subsequent extra depth of 50m costs £140 more to drill than the previous 50m.

a) Show that the cost of drilling to a depth of 500m is £11300.
b) The total sum of of money available for drilling is £76000. Find to the nearest 50m the greatest depth that can be drilled.
Reply 1
This is an Arithmetic Progression. (Strange as they were on my C2 last year.)

First term = 500
common difference = 140

You should have a number of formulae in your textbook into which you can plug these values. Sadly, my memory of them is vague. Perhaps someone else can enlighten you if you can't find them yourself. Sorry I can't be of more help.
Reply 2


:smile:
Reply 3
Or my nicer way of writing it (which is identical to the others but I don't like fractions) is ½n[2a+(n-1)d]
^ 1/2 is a fraction :confused:

Your way is identical to Jess's, just the 1/2 is infront instead of the "2" being underneath. It's like saying "I prefer 1/2 instead of 12\frac{1}{2}".
Reply 5
Exactly what he means!
Reply 6
Yeah, that's the one.
Reply 7
i keep trying but i can't can get right answer, can someone actually solve it. Thanks.......
Reply 8
Ok. You want to find how much it costs to drill to a depth of 500m. In the question, you are given how much the costs increase, in regards to the multiples of 50m. We know that when a further 50m is drilled, it costs an extra £140. So d = 140.

Think of this like an arithmetic progression, we know that the first term (when a depth of 50m is drilled) equals £500. So within the equation, a = 500.

We want to know how much it will cost when we drill to a depth of 500m. Think back to the question - we need to know what n is (ie which term it is in the sequence) - n = 500 /50 = 10.

Now try and solve it!
Reply 9
tnx jess for that i knew it was 10, but i kept it applying to the wrong formula, it's the "sum to to the 10 terms", that is the key.