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anonymous
 one year ago
I don't know what to do with this question, please help!
A piece of string 10m long is cut into pieces, so that the lengths of the pieces form an arithmetic sequence.
(i) The lengths of the longest and shortes pieces are 1m and 25cm respectively; how many pieces are there?
Answer:16
(ii) If the same string had been cut into 20 pieces with lengths that formed an arithmetic sequence, and if the length of the second longest had been 92.5 cm, how long would the shortest piece have been?
(ii) Is the one I don't know what to do with. I have already completed (i)
anonymous
 one year ago
I don't know what to do with this question, please help! A piece of string 10m long is cut into pieces, so that the lengths of the pieces form an arithmetic sequence. (i) The lengths of the longest and shortes pieces are 1m and 25cm respectively; how many pieces are there? Answer:16 (ii) If the same string had been cut into 20 pieces with lengths that formed an arithmetic sequence, and if the length of the second longest had been 92.5 cm, how long would the shortest piece have been? (ii) Is the one I don't know what to do with. I have already completed (i)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I need help with the last question please.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2Arithmetic Series: 2nd term = a1 + d where a = first term and d = common difference so here 92.5 = a1 + d

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2the sum of 10 terms = the length of the string = 10,000 cms

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2Now the sum of n terms is (n/2)[2a1 + (n  1)d] so here n = 20 and Sum = 10,000 so we have 10,000 = 10[2a1 + 19d]

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2so we have the system of equations a1 + d = 92.5 20a1 + 19d = 10,000

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, one little question why is it 2a1 ?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.22 * first term a1 will be the first term = shortest piece

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2so you need to find the value of a1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I use a different form of that equation normally so was confused for a second

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2if you multiply the first equation by 19 and add you can find a1

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2yes a1 is usually used in the US in UK we usually use just a

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a1 + d = 92.5 sorry, could you just explain more about how you got this part? I dont really understand why the first term plus the common term equals the second last term? I know I am missing something

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2oh  maybe i was wrong there sorry  i took that to be the second term  its the 19th term

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2also the total length = 1000 (wrong again!)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Haha, it happens! No worries.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2so the 2 equations are a1 + 18d = 92.5 20a1 + 19d = 1000

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, I am not sure I understand the concept behind that second equation

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2that is the formula for the sum of n terms of an arithmetic series Sn = (n/2)[2a1 + (n  1)d] here Sn = length of the string = 1000 cms, n = 20 (20 pieces) , a1 = first term, d = common difference

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok. Then I am meant to simultaneously solve those two equations?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2i bit messy Have you got a graphical calculator?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No I don't. Oh well, I will try it quickly now without one

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1is our shortest piece still 25cm?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No I don't think so. That was for the first question

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1how long should shortest piece ... forgot to read thru it all the way

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2hmm the results don't seem to give rational values..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah I am not getting anything that makes sense.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got d=2.5 a=47.625 after rounding

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2i thnk the equations are correct..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I probably just did something wrong then.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2yes the calc gives 47.631 and 2.4927

amistre64
 one year ago
Best ResponseYou've already chosen the best response.110m long 20(2a+19d)/2 = 1000 a+18d = 92.5 a is about 2.5, and d is about 5

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2yea my second equation was wrong 10(2a + 19d) = 201 + 190d

amistre64
 one year ago
Best ResponseYou've already chosen the best response.12a+19d = 100 a+18d = 92.5 2a +19d = 100 19/18a 19d = 19/18(92.5) a = (100(19/18(92+1/2)))/(2(19/18))

welshfella
 one year ago
Best ResponseYou've already chosen the best response.22.5 for shortest length and 5 for common difference

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2it was 190d not 19d

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2do you see the mistake I didnt distribute 10 over the (2a + 19) correctly

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2I thought someone would spot my deliberate mistake  oh amistre did!

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2good there is another formula for sum of n terms of an arithmetic series Sn = (n/2)[ a1 + L] where L is the last term If you know the last term its a lot simpler

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, thats the form I normally use and I didn't remeber about the other one not needing the last term which is a big part of why I got stuck I think Just trying to solve those two equations myself now.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.2probably best to multiply first one by 20 and add to get d first

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yup! Did it and got the two right answers! Thank you so much for your help!
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