Series math question. (1 Viewer)

[Shoom]

Heather decides to swim every day to improve her fitness level.On the first day she swims 750metres, and on each day after that she swims100metres more than the previous day.That is, she swims 850metres on thesecond day, 950metres on the third day and so on.(i)Write down a formula for the distance she swims on the nthday.(ii)How far does she swim on the 10thday?(iii)What is the total distance she swims in the first 10days?(iv)After how many days does the total distance she has swum equal thewidth of the English Channel, a distance of 34kilometres?

I can do the first three, please do them all for to make sure im doing them correctly, I dont know how to do the last one so please help.

 

[lyounamu]

Heather decides to swim every day to improve her fitness level.On the first day she swims 750metres, and on each day after that she swims100metres more than the previous day.That is, she swims 850metres on thesecond day, 950metres on the third day and so on.(i)Write down a formula for the distance she swims on the nthday.(ii)How far does she swim on the 10thday?(iii)What is the total distance she swims in the first 10days?(iv)After how many days does the total distance she has swum equal thewidth of the English Channel, a distance of 34kilometres?

I can do the first three, please do them all for to make sure im doing them correctly, I dont know how to do the last one so please help.

1. Tn = a+(n-1)d
Tn = 750 + (n-1)100

2. T10 = 750 +(10-1)100 = 1650

3. S10 = n/2(2a+(n-1)d) = 10/2 (1500 + 9 . 100) = 12000

4. Sn = n/2(2a+(n-1)d) = n/2(1500 + 100n - 100) = 700n + 50n^2
And 700n + 50n^2 = 34000
n^2 + 14n - 680 = 0
(n+34)(n-20) = 0
n = 20

 

[Shoom]

Thankyou, I havent learnt question three and four yet, im trying to teach myself.


btw do you know any books or websites that post the answers to the past exams?

 

[lyounamu]

Shouldn't this be in the Maths section?

You buy the Success One books which give you the solutions of the HSC exam papers if that's what you're looking for.

Doesn't really matter seeing that it's yr 11 stuff...

But the most approrpraite forum would be the maths forum but meh... he could also get help from here...

 

[Aerath]

You buy the Success One books which give you the solutions of the HSC exam papers if that's what you're looking for.

Or you could be cheap and get the answers off BoS.

 

[Timothy.Siu]

That could also work.

But I prefer the convenience of a Success One Book

i prefer the accuracy of it too :uhhuh: (not suggesting anything)

 

[shaon0]

Heather decides to swim every day to improve her fitness level.On the first day she swims 750metres, and on each day after that she swims100metres more than the previous day.That is, she swims 850metres on thesecond day, 950metres on the third day and so on.(i)Write down a formula for the distance she swims on the nthday.(ii)How far does she swim on the 10thday?(iii)What is the total distance she swims in the first 10days?(iv)After how many days does the total distance she has swum equal thewidth of the English Channel, a distance of 34kilometres?

I can do the first three, please do them all for to make sure im doing them correctly, I dont know how to do the last one so please help.

IS this from the HSC Mathematics 2007 exam?

 

[lyounamu]

IS this from the HSC Mathematics 2007 exam?

I don't think so. I have done that when posted here and then I have come across that again while doing past papers from 2005 to 1991.