testing header
Math Goodies is a free math help portal for students, teachers, and parents.
Free Math
Newsletter
 
 
Interactive Math Goodies Software

Buy Math Goodies Software
testing left nav
Math Forums @ Math Goodies
Math Forums @ Math Goodies
Home | Profile | Register | Active Topics | Members | Search | FAQ
 All Forums
 Homework Help Forums
 Algebra
 Patterns Assignment

Note: You must be registered in order to post a reply.
To register, click here. Registration is FREE!

Screensize:
UserName:
Password:
Format Mode:
Format: BoldItalicizedUnderlineStrikethrough Align LeftCenteredAlign Right Horizontal Rule Insert HyperlinkInsert EmailInsert Image Insert CodeInsert QuoteInsert List Insert Special Characters Insert Smilie
   
Message:
* HTML is OFF
* Forum Code is ON

Math Symbols
Squared [squared] Cubed [cubed] Square Root [sqrt] Cube Root [cbrt] Pi [pi]
Alpha [alpha] Beta [beta] Gamma [gamma] Theta [theta] Angle [angle]
Degrees [degrees] Times [times] Divide [divide] Less Than or Equal To [less-than] Greater Than or Equal To [greater-than]
Plus Minus [plus-minus] Integral [integral] Sum [sum] Sub 1 [sub-1] Sub 2 [sub-2]
Element Of [element-of] Union [union] Intersect [intersect] Subset [subset] Empty Set [empty-set]

  Check here to subscribe to this topic.
 
   

T O P I C    R E V I E W
Nadeshiko Posted - 09/21/2013 : 00:21:11
Hello! Please help me on this problem. I tried and I still don't know how to do it. I'm sorry but I forgot the work that I tried. I did it in my head. Sorry. Please help me with the problem below.

1
2 3
4 5 6 7
8 9 10 11...

Questions:
1. How many #'s in row 30?
2. What row is #200 in? Where is its position in that row?
3. What # does row 12 start with?
4. Where is #2015? Give row and position.
5. What does row 16 end with?

Patterns:
Write at least 3 patterns you notice from this assignment.

6   L A T E S T    R E P L I E S    (Newest First)
TchrWill Posted - 09/29/2013 : 11:05:42
the example shown should look like the following:

n...............1......2.....3.....4.....5......6.......nN
N...............3......9.....19....35....59....93.......Nn
1st Diff...........6.....10.....16....24....34
2nd Diff.............4.......6......8.....10
3rd Diff.................2......2......2
TchrWill Posted - 09/27/2013 : 09:51:46
In addition to the obvious pattern identified by the_hill1962, there are

1
2.3
4.5.6
7.8.9.10
11.12.13.14.15
16.17.18.19.20.21...yielding the series of

1.3.6.10.15.21... and 1.2.4.7.11.16...

A stretch might be
1
2. 3
4. 5. 6. 7
8. 9.10.11.12.13.14
15.16.17.18.19.20.21.22.23.24.25
26.27.28.29.30.31.32.33.34.35.36.37.38.39.40.41
42.43.44.45...

The first step is to derive the equation that defines each series.

For example, consider the sequence N = 3, 9, 19, 35, 59, 93...

An expression can be derived enabling the definition the nth term of any finite difference series, one where the nth differences are constant. The expression is a function of the number of successive differences required to reach the constant difference. If the first differences are constant, the expression is of the first order, i.e., N = an + b. If the second differences are constant, the expression is of the second order, i.e., N = an^2 + bn + c. Similarly, constant third differences derive from N = an^3 + bn^2 + cn + d.

Take the following example:
n.................1......2.....3.....4.....5......6.......nN.........NN.................3......9.....19....35....59....93.......Nn
1st Diff.............6.....10.....16....24....34
2nd Diff................4.......6......8.....10
3rd Diff....................2......2......2


Using the data points (n1, N1), (n2,N2), (n3,N3), etc., we substitute them into N = an^3 + bn^2 + cn + d as follows:
(n1,N1) = (1,3) produces a(1^3) + b(1^2) + c(1) + d = 3 or a + b + c + d = 3
(n2,N2) = (2,9) produces a(2^3) + b(2^2) + c(2) + d = 9 or 8a + 4b + 2c + d = 9
(n3,N3) = (3,19) produces a(3^3) + b(3^2) + c(3) + d = 19 or 27a + 9b + 3c + d = 19
(n4,N4) = (4,35) produces a(4^3) + b(4^2) + c(4) + d = 35 or 64a + 16b + 4c + d = 35
Subtracting each successive pair yields
7a + 3b + c = 6
19a + 5b + c = 10
37a + 7b + c = 16
Again, subtracting each successive pair yields
12a + 2b = 4
18a + 2b = 6

Subtracting these yields 6a = 2 making a = 1/3, b = 0, c = 11/3, and d = -1 resulting in our final expression for the nth term of this series Nn = (n^3)/3 + (11n)/3 - 1 = (n^3 + 11n - 3)/3.
Checking it out for the 6th term we have [(6^3) + (66) - 3]/3 = [216 + 66 - 3]/3 = 279/3 = 93.

Now you can explore other derived series.
Questions:
1. How many #'s in row 30?
2. What row is #200 in? Where is its position in that row?
3. What # does row 12 start with?
4. Where is #2015? Give row and position.
5. What does row 16 end with?
the_hill1962 Posted - 09/25/2013 : 18:02:42
I wondered the same thing, TchrWill.
Since Nadeshiko has not replied, I think it might be a troll.
The problem is impossible as stated. There is no pattern.
Maybe if it is a real person, obviously a lazy one since no work or thoughts on how to start it.
So, the three dots could be Nadeshiko's way of saying there are more numbers but I am too lazy to type them.

Maybe the pattern is

1
2 3
4 5 6 7
8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
and so on...

Now, there is something to work with.
However, since Nadeshiko has not even commented, I don't think we should discuss the problem further except for showing what the next lines are.
32 33 34 35... ...61 62 63
64 65 66... ...126 127
.
.
.
TchrWill Posted - 09/25/2013 : 16:25:19
quote:
Originally posted by Nadeshiko

Hello! Please help me on this problem. I tried and I still don't know how to do it. I'm sorry but I forgot the work that I tried. I did it in my head. Sorry. Please help me with the problem below.

1
2 3
4 5 6 7
8 9 10 11...

Questions:
1. How many #'s in row 30?
2. What row is #200 in? Where is its position in that row?
3. What # does row 12 start with?
4. Where is #2015? Give row and position.
5. What does row 16 end with?

Patterns:
Write at least 3 patterns you notice from this assignment.




Are you sure of the pattern you offer? Might it really be

1
2.3
4.5.6
7.8.9.10.

What series do the last digits in each row form?
royhaas Posted - 09/23/2013 : 12:03:29
I wish teachers would quit assigning these things. All they show is that a teacher has a pre-conceived notion of a pattern, and shows ignorance of number theory and finite differences.
Ultraglide Posted - 09/23/2013 : 11:37:38
You need to show your work.

Math Forums @ Math Goodies © 2000-2004 Snitz Communications Go To Top Of Page
This page was generated in 0.29 seconds. Snitz Forums 2000
testing footer
About Us | Contact Us | Advertise with Us | Facebook | Blog | Recommend This Page




Copyright © 1998-2014 Mrs. Glosser's Math Goodies. All Rights Reserved.

A Hotchalk/Glam Partner Site - Last Modified 30 Oct 2014