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sandra wrote the sequence below
2,5,10,17,...
which equation represents the rule for finding the nth term of this equation

  • math -

    did you notice that each term is one larger than a perfect square, ....

    2 = 1^2 + 1
    5 = 2^2 + 1
    10 = 3^2 + 1
    17 = 4^2 + 1
    .
    .


    so what do you think?

  • math -

    The numbers are increasing by 3 then 5 then 7 then 9. Next, notice that every number is actually one more than a square number.

    So the general formula is:

    a(n)=1+n^2

    Let's check:

    a(1)=1+1^2=1+1=2

    a(2)=1+2^2=1+4=5

    a(3)=1+3^2=1+9=10

    a(4)=1+4^2=1+16=17

    We see it's correct.

    The next numbers in the sequence should be:

    a(5)=1+5^2=1+25=26

    a(6)=1+6^2=1+36=37 etc.

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