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C1 Exam Question

Prospectors are drilling for oil. The cost of Drilling to a depth of 50m is £500. To Drill a further 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 money available for drilling is £76000. Find, to the nearest 50m, the greatest depth that can be drilled.

Reply 1

sonofdot

Can you see that this is an arithmetic progression with first term 1140 and common difference 140?

Reply 2

Bonz0

every 50m is £500 + (n-1)x140. it is effectively an AP

Reply 3

Da_hopeful_1

yeh i got that bit Furthermore i've done part A, but it's just part B where i got stuck as i get a quadratic formula but don't know how to solve it. If anyone can show their workin out for part B then it would be greatly appreciated

Reply 4

sonofdot

Da_hopeful_1

Why don't you post your working so far - then I will be easier to see if/where you are going wrong? :smile:

Reply 5

Da_hopeful_1

Okay sure,

I hope u can understand it.

Sum = £76000

a = £500
d = £140

S = n/2 [2a + (n-1)d ]

76000 = n/2 [ 1000 + (n-1) 140 ]

Reply 6

v1oXx-

Starting multiplying it out. :rolleyes:

Reply 7

Da_hopeful_1

It doesn't work. How do you go on from their :s-smilie:

Reply 8

sonofdot

Da_hopeful_1

Okay sure,

I hope u can understand it.

Sum = £76000

a = £500
d = £140

S = n/2 [2a + (n-1)d ]

76000 = n/2 [ 1000 + (n-1) 140 ]

Ok: here's the problem. The question isn't about a sum, its about a term in the sequence.

Let me explain: The sequence 1140, 1280, 1420... is the amount of money it takes to drill 100, 150, 200m

So if the nth term in the sequence equals 76000, then they've drilled (100+50n)m

So

u_n = a + (n-1)d

Put U_n equal to 76000 and then solve for n

Reply 9

Da_hopeful_1

what do n and d equal in the formula

Reply 10

v1oXx-

d =140,
n is what you are trying to find.

you will get a equation which you'll need to factorize to find n.

Reply 11

akshayv2

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