1. Suppose you have a sequence that begins {3, 8, 13, 18}. Give the next 3 numbers in your sequence. Use a recursive definition to define your sequence.

Question

I have watched 2 Youtube videos on how to write recursive definition and I can not understand it. Could anyone answer this so I can have an example to go off of.

Answer 1

Hello Cayce,

 

For the given sequence, the common difference is d = 5.

 

Let a₁ be the first term: a₁ = 3.

Then a₂ = a₁ + 5 → a₂ = 3 + 5 = 8,

and a₃ = a₂ + 5 → a₃ = 8 + 5 = 13,

and a₄ = a₃ + 5 → a₄ = 13 + 5 = 18, etc...

 

So, to get from one term to the next (recursively), you take the previous term, and add the common difference of 5.

 

This looks like

a_n = a_n-1 + 5.

 

But since there is no term before the first term, you have to state the first term as part of the recursive definition.  That is,

 

a₁ = 3

a_n = a_n-1 + 5.

 

I hope the above helps, and thank you for posting the question.

 

Michael Ehlers