Suppose you have a sequence that begins {1, 3, 9, 27}.Give the next 3 numbers in your sequence. Use a recursive definition to define your sequence.

Question

With this equation I got I think I may be wrong. Want to double check myself

 

A1= 3

 

An=3(3) to the power of 2

Answer 1

You are correct about the nature of the sequence. A recursive definition defines each term by the preceding term. In this case, a recursive definition would be A_n=3 x A_n-1 because each term is three times the preceding one.

 

An explicit definition would be A_n=3^n-1 because the first term is 3⁰, the second is 3¹, the third is 3², and so on.

Answer 2

Recursive Definition: 3ⁿ=x

 

Where n is an integer n=1,2,3,4,.... and x is the next number in your sequence. 

 

For n=0, x=1

For n=1, x=3

For n=2, x=9

For n=3, x=27

For n=4, x=81

For n=5, x=243

For n=6, x=729