Question

Please help me with this problem that my son an I are stuck on were not understand what we did wrong. 3.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?Answer:

Answer 1

You have the following sequence:

6, 18, 54, 162, ...

You can notice that each element (except the first one) is three times the previous one. Then, for the recursive rule you have:

a) recursive rule:

`a_n=3\cdot a_(n-1)`

Based on the previous result, you can conclude for the iterative rule:

b) iterative rule:

`a_n=6\cdot3^(n-1)`

If you replace n by the index of each element you obtain the given sequence.