### Home > CCAA8 > Chapter 11 Unit 12 > Lesson CCA: 11.2.2 > Problem 11-47

Find an equation for each sequence.

*n**t*(*n*)To find the equation, you need to know the initial term, when

.When

,, and when,, so you know that it decreases byfrom 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.

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.