Aubrey M.

asked • 06/16/17

Which of the following is an example of a recursive sequence? 2, 5, 8, 11, ... 1, 3, 9, 27, ... 2, 4, 6, 10, ...

 How do you find the answer to thus question and can you show the steps to answering this question. 

2 Answers By Expert Tutors

By:

Mark M. answered • 06/16/17

Mathematics Teacher - NCLB Highly Qualified

Michael J.

The definition of recursive is
 
an = an - 1 + d
 
Rearranging the formula, we get
 
an - an - 1 = d
 
This is a common difference between 2 consecutive numbers.  Therefore,
 
1 , 5 , 8, 11    is recursive.
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06/16/17

Mark M.

tutor
Your presentation is defining the sequence using a recursive formula. It does not make the sequence recursive.
For a more detailed explanation go to PurpleMath.com and search for recursive sequence.
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06/16/17

Michael J.

I took your advise and looked up recursive sequence.  I believe it is safe to say that recursive formula and recursive sequence are commonly confused with each other.
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06/16/17

Mark M.

tutor
It is an esoteric distinction. Mathematicians are rather parsimonious with words. Too often the same word has different meanings depending on context/position.
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06/17/17

Shenita P. answered • 06/16/17

Math is my passion

Mark M.

tutor
You provide the recursive formula for an arithmetic sequence. That does not make the sequence recursive.
http://www.purplemath.com/modules/nextnumb3.htm
The second sequence is geometric - which can also be defined recursively although it is not recursive.
The third sequence is neither.
 
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06/16/17

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