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Math Help - recursive formula

  1. #1
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    recursive formula

    Hiya I need give a recursive formula for the numbers 1,3,6,10,15,21,34

    I found an+1=an+2n+1

    Is this right?, and if it isnt what did i do wrong

    I also need to give a formula for n in the number series but that excapes me, any ideas or clues would be helpful, Thanks
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  2. #2
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    Quote Originally Posted by JBswe View Post
    Hiya I need give a recursive formula for the numbers 1,3,6,10,15,21,34

    I found an+1=an+2n+1

    Is this right?, and if it isnt what did i do wrong

    I also need to give a formula for n in the number series but that excapes me, any ideas or clues would be helpful, Thanks
    Obviously it's not right - a simple substitution of values of n reveals that in short order.

    Observe the pattern:

    a_2 - a_1 = 3 - 1 = 2

    a_3 - a_2 = 6 - 3 = 3

    a_4 - a_3 = 10 - 6 = 4

    Clearly:

    a_n - a_{n-1} = n

    Therefore:

    a_{n+1} - a_n = n + 1 \therefore a_{n+1} = a_n + n + 1, where a_1 = 1. The coefficient of n is 1, NOT 2.

    a_{n+1} - a_n = n + 1 is a recurrence relation - there are standard techniques for solving a_n in terms of n ......
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