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C-27.

Find an equation for each sequence. Homework Help ✎

  1. To find the equation, you need to know the initial term, when .

    When , , and when , , so you know that it decreases by from one term to the next.

    To find the number before , you add , because was taken away to get . So the initial term is .

    To get the number after , you take away once. To get the next number, you take away again. To get the next number you take away again. Since you are always subtracting , you multiply by to represent how many times you have subtracted . Now write your equation.


  1. Year

    Cost

    This sequence is different than the one in part (a). You multiply instead of subtract.

    The cost was in Year , but you need to know how much it was in Year to write the equation. Each year it is multiplied by . So the cost in Year is times what it was in Year , which is times what it was in Year . So if you divide the cost in Year by , you will have the cost from Year .

    Similar to part (a), because you are always multiplying by , you can use a variable as the exponent of to represent how many times you have multiplied by . Now write your equation.