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Growth Problem

  • 17-10-2018 6:47pm
    #1
    auspicious
    Registered Users Posts: 4,497 ✭✭✭


    Initial value is 10
    There are 50 periods.
    In the first period, 10 is the added value.
    Each successive period, the added value increases by 10

    period 1 is 10 + 10 = 20
    period 2 20 + 20 = 40
    3. 40 + 30 = 70
    4. 70 + 40 = 110

    What is the final figure after 50 periods?


Comments

  • #2
    Horusire
    Registered Users Posts: 158 ✭✭Horusire


    auspicious wrote: »
    Initial value is 10
    There are 50 periods.
    In the first period, 10 is the added value.
    Each successive period, the added value increases by 10

    period 1 is 10 + 10 = 20
    period 2 20 + 20 = 40
    3. 40 + 30 = 70
    4. 70 + 40 = 110

    What is the final figure after 50 periods?

    Is this the 49th term in the fibonacci sequence with an added zero?


  • #3
    auspicious
    Registered Users Posts: 4,497 ✭✭✭auspicious


    It's not homework. It's something I've been pondering over the past hour or so.
    And I think the fibonacci sequence does not work here.
    Surely there is an equation.
    Or is it just a matter of laborious addition?

    Thanks.


  • #4
    MathsManiac
    Registered Users Posts: 1,595 ✭✭✭MathsManiac


    You could do it by laborious addition, but there is a better way.

    Note the following:

    The thing you're adding on each time is increasing by a fixed amount. That means that the sequence of things you're adding on is an arithmetic sequence.

    Look up arithmetic sequence, and, particular, sum to n terms of an arithmetic sequence, and you should be able to work it out. Come back if you need more help.


  • #5
    auspicious
    Registered Users Posts: 4,497 ✭✭✭auspicious


    g (n) = 5n^2 +5n + 10

    Input:
    Table[5 n^2 + 5 n + 10, {n, 1, 50}]

    Result
    {20, 40, 70, 110, 160, 220, 290, 370, 460, 560, 670, 790, 920, 1060, 1210, 1370, 1540, 1720, 1910, 2110, 2320, 2540, 2770, 3010, 3260, 3520, 3790, 4070, 4360, 4660, 4970, 5290, 5620, 5960, 6310, 6670, 7040, 7420, 7810, 8210, 8620, 9040, 9470, 9910, 10360, 10820, 11290, 11770, 12260, 12760}


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