20 points

view the sequence:

6,18,54,

a.) what is the recursive rule for the sequence?

b.) what is the iterative rule for this sequence?

A.)

2 * 3 = 6

6 * 3 = 18

18 * 3 = 54

54 * 3 = 162

B.) The answer is 3x more, each step goes up times 3.

As you can see, 2 is the first term in the sequence.  Multiplying the current term by the common ratio, which is 3, presents the next term.  Then that term is multiplied by the common ratio to present the term after it.

an + 1 = 3an

or you can write

an = 3an - 1

where:

an is the new term ,

an - 1 is the preceding term

Notice that we can write the following formula as :

an / (an - 1) = 3

This shows that the ratio between the new term to preceding term is 3.

Hope this helps.