math grade 6 number patterns, need help please

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confusedmom

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Sep 12, 2009
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hi and thanks in advance for looking this over. My son is in grade 6 and he is starting to do number patterns. I've been able to i'm able to do recursive patterns but this one is driving me nuts. I dont think its recursive and the answer that I get just seems crazy for an 11 year old to figure out.
Here is the question.

1. write the next three terms in this number pattern.
What is changing each time? Explain.
1,3,5,9,15,25,...


so there is the question that has me stumped. I've tried everything my brain could think up and I'm starting to feel pretty stupid at this point.
All I could come up with was a weird pattern of
1+2
3+2
5+4
9+4+2
15+2+4+4
25+2+2+4+4
with the next ones being
37+2+2+4+4+2
51+2+4+4+2+2+4
69

trying to check it i got this
69-51=18
51-37=14
37-25=12
25-15=10
15-9=6
9-5=4
5-3=2
3-1=2
which lead me to 2 2 4 6 10 12 14 18
which lead me to 2 2 4 4 2 2 4

so that is where I got the pattern of 2244224 what is changing each time? I'm confusing myself lol.
But for an 11 year old to figure this out, I have to have done something wrong. PLEASE HELP ME so I can help my son.
sorry if this doesn't make sense.

thanks again, Beth aka confused mom
 
confusedmom said:
… i'm able to do recursive patterns …
Click to expand...


It's good that you understand recursive sequence definitions because the sequence {1,3,5,9,15,25,…} looks recursive, to me.

Add the first two elements in the sequence. Compare that sum with the third element.

Add the second and third elements in the sequence. Compare that sum with the fourth element.

Add the third and fourth elements in the sequence. Compare that sum with the fifth element.

See the recursive pattern? 8-)

 
confusedmom said:
1. write the next three terms in this number pattern.
What is changing each time? Explain.
1,3,5,9,15,25,...
Click to expand...
Beth, look at the differences:
1[2]3[2]5[4]9[6]15[10]25 ; a difference is the sum of the 2 previous differences (starting at [4])

So next term will be 41: (25 + 6 + 10). You with me?

EDIT: better look at Mark's; much simpler than mine !
 
oh my gosh. LOL
you made it soooo easy.
You would laugh at how long I spent trying to figure that one out. seriously I've been fooling around with this one since 6:30pm till now lol.
I'm so glad I found this site. Thank you so much!!!

so is it still a recursive pattern if you add the numbers together and add 1?
I thought a recursive pattern was when the numbers can be found by applying the pattern rule to the previous number.

so if you add 1(+3 ) then add 1
then 3(+5 )then add 1
then 5(+9 ) then add 1
and continue .... would that still make it recursive even though the first number ( the one in brackets) your adding to it is different each time.

I was thinking a recursive pattern was more like 2,4,10,28,32,244,730,2188
using x3 , -2 as a pattern rule.

sorry for the extra question. I'm just trying to figure out how to teach this to my son when he comes home with his math book and no clue. :)
 


There might be more than one sequence containing these first six elements.

I noticed that each of these elements is of the form 3^n * 5^m.

With n and m representing all possible pairs of Whole numbers, we could continue the sequence as follows.

{1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 125, 135, 225, …}

Please don't ask me to write a formula for this one. :wink:

 
Denis, I understand your post to . Oh my goodness you guys are making me sooooo happy. I just called my 11 year old in to show him and he was happy it wasn't as hard as I was making it before. You guys are a life savers :)
When I was a kid I had such a hard time with math. I just want to be able to help my son and make it fun for him.
This site is GREAT!!!
 
confusedmom said:
… I thought a recursive pattern was when the numbers can be found by applying the pattern rule to the previous number …
Click to expand...


Recursive formulas can use any number of previous elements. In other words, we're not limited to using only the previous element, in a recursive definition.

Also, we often need to define the first few elements, in a recursive definition.

I realize that your son's exercise does not require writing a definition, but here it is anyways:

a(1) = 1

a(2) = 3

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

n > 2

8-)

 
mmmmbot Ok now you've got me confused lol. I think i'll just go with the first answer you gave me since I understood that one :wink:
 


Go with what you understand, and ignore the rest. 8-)

I was just explaining that recursive patterns can include any number of previous elements (as well as additional constants), and I showed how the formula for this particular sequence includes the previous two elements.

According to the exercise, your son does not need to write the formula.

The notation is probably Greek, to you, because you've never seen it. I apologize; I should have realized that such formulas are beyond the sixth grade level. (Something for your son to expect in high school, perhaps.)

 
These "patterns" series can get silly; anybody can make one up.

I write down 1,2,3 ; 1 * 2 + 3 = 5 ; so
[1]1, [2]2, [3]3, [4]5, [5]11, [6]26, [7]?
The term number is shown in [].

So term[7] = term[4] * term[5] + term[6] = term[7-3] * term[7-2] + term[7-1] = 81

If we let term number be represented by n, then in above the question would be:
find term [n] where n = 7

So now you can see that "formula" for finding any term [n] is: a[n] = a[n-3] * a[n-2] + a[n-1]
 
confusedmom said:
hi and thanks in advance for looking this over. My son is in grade 6 and he is starting to do number patterns. I've been able to i'm able to do recursive patterns but this one is driving me nuts. I dont think its recursive and the answer that I get just seems crazy for an 11 year old to figure out.
Here is the question.

1. write the next three terms in this number pattern.
What is changing each time? Explain.
1,3,5,9,15,25,...


so there is the question that has me stumped. I've tried everything my brain could think up and I'm starting to feel pretty stupid at this point.
All I could come up with was a weird pattern of
1+2
3+2
5+4
9+4+2
15+2+4+4
25+2+2+4+4
with the next ones being
37+2+2+4+4+2
51+2+4+4+2+2+4
69

trying to check it i got this
69-51=18
51-37=14
37-25=12
25-15=10
15-9=6
9-5=4
5-3=2
3-1=2
which lead me to 2 2 4 6 10 12 14 18
which lead me to 2 2 4 4 2 2 4

so that is where I got the pattern of 2244224 what is changing each time? I'm confusing myself lol.
But for an 11 year old to figure this out, I have to have done something wrong. PLEASE HELP ME so I can help my son.
sorry if this doesn't make sense.

thanks again, Beth aka confused mom
Click to expand...

In the absence of further explanation - the answer can be any number - say 42 following a sixth order polynomial equation. Of course a sixth-grader will not be expected to find that (- but who knows there could be Gauss or Ramanujan in that class). I hate these problems - where you are reduced to guessing what did the teacher have in mind???
 
Hello, confusedmom!

1. Write the next three terms in this number pattern: .\(\displaystyle 1,\:3,\:5,\:9,\:15,\:25,\:\hdots\)
What is changing each time? .Explain.
Click to expand...

mmm444bot has the answer.

Starting with the third term, each term is the sum of the preceding two terms, plus 1.

. . \(\displaystyle \begin{array}{ccccccccccccccccccc}1 &\qquad\quad & 3 && 5&& 9 && 15 && 26 && \boxed{42} && \boxed{69} && \boxed{112}\\ &&& ^{(1+3)+1\:\nearrow} && ^{(3+5)+1\:\nearrow} && ^{(5+9)+1\:\nearrow} && ^{(9+15)+1\:\nearrow} && ^{(15+26)+1\:\nearrow} && ^{(26+42)+1\:\nearrow}} && ^{(42+69)+1 \:\nearrow} \end{array}\)

 
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