Question

PLEASE HELP 20 POINTS

View the sequence:

6,18,54,162...

A.) What is the recursive rule for the sequence?

B.) What is the iterative rule for this sequence?

Answer 1

a)

`a_n=3.a_(n-1)`

`a_1=6`

b)

`a_n=6(3)^(n-1)`

Explanation:

Recursive And Iterative Rules For Sequences

The recursive rules allow finding terms of a sequence as a function of the previous one. The iterative rules provide a formula to compute the n-th term without the need to compute the previous terms.

Our sequence goes like 6,18,54,162... It can be found that any term equals the previous one by 3

a) The recursive rule can be deducted from the above sentence

`a_n=3.a_(n-1)`

`a_1=6`

It's important to provide the first term where the rule will eventually stop

b) The iterative rule is found with the help of geometric sequences

`a_n=a_1r^(n-1)`

With
`a_1=6` and r=3

`a_n=6(3)^(n-1)`