write a recursive formula that generates the terms: 1,3,9,27,...

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Matthew Fonda eNotes educator| Certified Educator

I want to elaborate a bit more on how to find this. When working on a problem involving a sequence, a good first step is to look at the numbers and see if anything stands out. For this sequence, we notice that each term is three raised to the nth power.

`a_n = 3^n`

This is not a recursive formula, but from this point it is easier to see how to find one. Let's think about what is `a_(n+1)` ? Well, let's plug `n+1` into our formula above:

`a_(n+1) = 3^(n+1) = 3*3^n = 3*a_n`

Therefore we can conclue that

`a_(n+1) = 3*a_n` , or ` a_n = 3*a_(n-1)`


embizze eNotes educator| Certified Educator

Write a recursive formula that generates the terms 1,3,9,27,...

A recursive formula defines a given term of a sequence in terms of previous terms.

For this sequence, let `a_1=1` , and `a_n=a_(n-1)*3` for `n>1` .