Find an equation for each sequence. Homework Help ✎
To find the equation, you need to know the initial term, 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.
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.