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Math Help - Arithmetic sequence

  1. #1
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    Arithmetic sequence

    Vivienne starts counting going by 3s from 4:
    4,7,10,13.
    Chloe starts counting backwards from 744 by 7s:
    744, 737, 730, 723
    They start saying their sequences at the same time and simultaneously say one number every second
    i)What is the difference between the 7th numbers they both say?
    (Using the arithmetic sequence formula) I got 682 which is not the right answer ><
    ii)Which number do they both say at the same time?
    I need some help with this question, thank you for any help given
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  2. #2
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    Quote Originally Posted by christina View Post
    Vivienne starts counting going by 3s from 4:
    4,7,10,13….
    Chloe starts
    counting backwards from 744 by 7s:
    744, 737, 730, 723
    They start saying their sequences at the same time and simultaneously say one number every second
    i)What is the difference between the 7th numbers they both say?
    (Using the arithmetic sequence formula) – I got 682 which is not the right answer ><
    ii)Which number do they both say at the same time?
    I need some help with this question, thank you for any help given
    Use the formula for the nth term of an arithmetic sequence U_n = a+(n-1)d. For example

    U_7 = a+6d


    Spoiler:
    Chloe: U_7 = 744-42 = 702
    Viv : U_7 = 4 + 18 = 22

    Difference is 702-28 = 674


    ii) U_n = 4+3n-3 = 3n+1

    U_n = 744-7n+7 = 751-7n

    They will be equal and solve for n=75
    Last edited by e^(i*pi); January 10th 2010 at 04:45 AM.
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  3. #3
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    Quote Originally Posted by christina View Post
    Vivienne starts counting going by 3s from 4:
    4,7,10,13.
    Chloe starts counting backwards from 744 by 7s:
    744, 737, 730, 723
    They start saying their sequences at the same time and simultaneously say one number every second
    i)What is the difference between the 7th numbers they both say?
    (Using the arithmetic sequence formula) I got 682 which is not the right answer ><
    ii)Which number do they both say at the same time?
    I need some help with this question, thank you for any help given
    First sequence:

    t_n = 4 + 3(n - 1)

    so t_7 = 4 + 3(7 - 1)

     = 22.


    Second sequence:

    t_n = 744 - 7(n - 1)

    so t_7 = 744 - 7(7 - 1)

     = 702.


    So the difference between them is 702 - 22 = 680.
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  4. #4
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    Quote Originally Posted by e^(i*pi) View Post
    Use the formula for the nth term of an arithmetic sequence U_n = a+(n-1)d. For example

    U_7 = a+6d


    Spoiler:
    Chloe: U_7 = 744-42 = 702
    Viv : U_7 = 4 + 24 = 28

    Difference is 702-28 = 674


    ii) U_n = 4+3n-3 = 3n+1

    U_n = 744-7n+7 = 751-7n

    They will be equal and solve for n=75
    Actually Viv's is

    U_n = 4 + 3(n - 1)

    U_7 = 4 + 3(7 - 1)

     = 22.
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  5. #5
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Prove It View Post
    Actually Viv's is

    U_n = 4 + 3(n - 1)

    U_7 = 4 + 3(7 - 1)

     = 22.
    Yeah it is, for some reason I put the common difference as 4
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  6. #6
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    Quote Originally Posted by christina View Post
    Vivienne starts counting going by 3s from 4:
    4,7,10,13….
    Chloe starts counting backwards from 744 by 7s:
    744, 737, 730, 723
    They start saying their sequences at the same time and simultaneously say one number every second
    i)What is the difference between the 7th numbers they both say?
    (Using the arithmetic sequence formula) – I got 682 which is not the right answer ><
    ii)Which number do they both say at the same time?
    I need some help with this question, thank you for any help given
    Since they are saying the numbers at intervals of one second, they will say a_n and b_n at second "n". The first sequence, as other have told you is a_n= 4+ 3(n-1) and the other is b_n= 774- 5(n-1).

    To find the number they say both say at the same time, solve a_n= 4+ 3(n-1)= 774- 5(n-1)= b_n for n, then put it into either of the formulas to find the number.
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  7. #7
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    thank you so much for all your help guys ! i really appreciate it ^^
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