Mark M. answered • 06/16/17

Mathematics Teacher - NCLB Highly Qualified

Mark M.

06/16/17

Michael J.

06/16/17

Mark M.

06/17/17

Aubrey M.

asked • 06/16/17 How do you find the answer to thus question and can you show the steps to answering this question.

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Mark M. answered • 06/16/17

Mathematics Teacher - NCLB Highly Qualified

2, 5, 8, 11 ... is an arithmetic sequence. And while it can be defined with a recursive formula, it is not a recursive sequence.

1, 3, 9, 27 ... is a geometric sequence. It also is not a recursive sequence.

A recursive sequence is one in which each successive term is determined by another sequence.

E.g., 1, 3, 6, 10, 15, .. The pattern is +1, +2, +3, +4, +5

Another (more famous) recursive sequence is

1, 1, 2, 3, 5, 8, 13, 21, 34, ...

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

An example of a recursive sequence would be 2,5,8,11 because in accordance to the recursive formula this sequence is accurate

Recursive formula

a(n)= a(n-1)+B

a(1)= first term

B= The same amount being added each time which in this case is 3

so, a(n)= a(n-1)+B

a(2)= a(2-1) +3

=a(1)+3

=2+3

=5

Next

a(3)=a(3-1)+3

=a(2)+3

=5+3

=8

a(4)=a(4-1)+3

=a(3)+3

=8+3

=11

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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Michael J.

_{n}= a_{n - 1}+ d_{n}- a_{n - 1}= d06/16/17