The sequence 6, 18, 54, 162, ... shows the number of pushups Kendall did each week, starting with her first week of exercising.

(a) What is the recursive rule for the sequence?

(b) What is the iterative rule for the sequence?

The iterative rule for the sequence is

tn = 6*3^ (n - 1)

The recursive rule I find to be a little harder, but it is very useful in computer science. f (n) = 3*f (n - 1) So if you now what f (n - 1) is then you can find f (n).

So for f (1) we have 6

for f (2) we have f (1) * 3

f (2) = 6 * 3 = 18

for f (3) we have

f (3) = 3 * f (n - 1)

f (3) = 3 * f (2)

f (3) = 3*18

f (3) = 54