algebra

A rare bacterial culture is being grown in a lab. As the days progress, the cells multiply and grow.

After 1 day, there is only 1 cell.
After 2 days, there are 9 cells.
After 3 days, there are 20 cells.
After 4 days, there are 34 cells.

Which recursive equation represents the pattern?

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  1. What are your choices?

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  2. an=an-1+3n

    an=an-1+(n+2)

    an=an-1+3(n+2)

    an=an-1+(3n+2)

    I thought it was the last one but am not sure and am trying to help my grandson.

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  3. well, the amounts added are 8,11,14
    They differ by 3, so it will look like

    a(n) = a(n-1) + 3n + ?

    3n looks like 3,6,9, so we have

    a(n) = a(n-1) + 3(n-1)+5 = a(n-1)+(3n+2)

    so you are correct

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  4. thank you

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