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C2: wordy question (sequences and series) watch

1. Hi everyone,

I've got a wordy question and I can't get anywhere near the right answer. Would someone be able to help me please?

The question is:

A pipeline is to be constructed under a lkae. First mile takes 15 days to construct. Each further mile will take 3 days longer than the one before.

a)Find the nth term. A: 3n + 12
b)show that the total time taken to complete the first n miles is (3/2)n(n+9) days (I did this).

C is the part I'm struggling with:
c) Calculate the total length of pipeline that can be constructed in 600 days.

I tried a few different approaches such as 15 + (n-1)3=600 and also using 600 as the answer for the sum of n terms, but neither gave me the correct answer. Could anyone suggest the right approach?

Thanks
Marc.
2. (Original post by marcsaccount)
Hi everyone,

I've got a wordy question and I can't get anywhere near the right answer. Would someone be able to help me please?

The question is:

A pipeline is to be constructed under a lkae. First mile takes 15 days to construct. Each further mile will take 3 days longer than the one before.

a)Find the nth term. A: 3n + 12
b)show that the total time taken to complete the first n miles is (3/2)n(n+9) days (I did this).

C is the part I'm struggling with:
c) Calculate the total length of pipeline that can be constructed in 600 days.

I tried a few different approaches such as 15 + (n-1)3=600 and also using 600 as the answer for the sum of n terms, but neither gave me the correct answer. Could anyone suggest the right approach?

Thanks
Marc.
Equating (3/2)n(n+9) to 600 and solving should work. Can you post your working and the answer you're trying to reach?
3. Hi again notneck - thanks for your help. The correct answer is 16 miles.

(3/2)n(n+9) = 600

n(n+9)= 400

n^2 + 9n = 400

...so then I thought I had to factor, but c=0, so I can't, can I?
4. (Original post by marcsaccount)
Hi again notneck - thanks for your help. The correct answer is 16 miles.

(3/2)n(n+9) = 600

n(n+9)= 400

n^2 + 9n = 400

...so then I thought I had to factor, but c=0, so I can't, can I?
Move the 400 to the left then you have

n^2 + 9n - 400 = 0

This is a quadratic in the form that you should be used to. You can solve it by factorising or using the quadratic formula if you can't factorise it.
5. (Original post by marcsaccount)
Hi again notneck - thanks for your help. The correct answer is 16 miles.

(3/2)n(n+9) = 600

n(n+9)= 400

n^2 + 9n = 400

...so then I thought I had to factor, but c=0, so I can't, can I?
If you rewrite it as n^2 + 9n - 400 = 0 then c certainly isn't 0
6. Sorry notneck, I can factorise it. But my problems today are things I'm perfectly comfortable with but for some reason I've not spotted them. I must be tired. Thanks so much for your help.

Marc

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