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State the rule for this pattern:

What about: subtract the last number and add 2 to the next term

  • Math -

    using your rule, do you get the given sequence?

    Here's a method of attack:
    You know that 1+3+5+...+n = n^2
    adding up the 1st n odd numbers gives you n^2.

    In your sequence, you have
    1 1+4 1+4+6 1+4+6+8
    which looks very similar. So, expect something with n^2 in it.

    1 = 2^2-3
    5 = 3^2-4
    11 = 4^2-5
    19 = 5^2-6

    So, it looks to me like

    Tn = (n+1)^2 - (n+2) = n^2+n-1

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