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Math Help - Rate of increase

  1. #1
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    Rate of increase

    If I have two sequences A&B with starting points at t=0 of 5 and 8 respectively, then sequence A increases by 3 and sequence B by 2. i.ie

    A: 5,8,11,14,17
    B: 8,10,12,14,16

    Ok so I know that at some stage sequence A will 'overtake' sequence B (as its increasing at a faster rate) at some stage (t=4 in the example ive thought up) but without writing out every number how can I just see or tell that at t=4 sequence A will 'overtake' sequence B.

    Lcm? percentages? Im after the method?
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  2. #2
    Super Member Quacky's Avatar
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    Re: Rate of increase

    You can do it by setting up an equation for the nth term of a sequence.

    The "general term", t of a sequence will be compared to the placement of the numbers in the sequence, n.

    As sequence 1 increases at a rate of 3, t=3n+k, where k is an unknown integer that we still need to work out. When n=1, t=5. Substituting this into the equation gives 5=3+k, so k=2 and the equation I was looking for is t=3n+2. You can check this by substituting in the other numbers of the sequence. Ie, when n is 2, does t=8?

    If you do the same for the bottom sequence, then you have two simultaneous equations. You need to solve these for n.
    Last edited by Quacky; January 16th 2012 at 10:59 AM.
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  3. #3
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    Re: Rate of increase

    how could i be so thick grr thanks.
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