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 Goodies on facebook

Math Goodies Blog
Math Forums @ Math Goodies
Math Forums @ Math Goodies
Home | Profile | Active Topics | Members | Search | FAQ
 All Forums
 Homework Help Forums
 Algebra
 Patterns Assignment

Note: You must be registered in order to post a reply.

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 0.04 seconds. Snitz Forums 2000
testing footer
About Us | Contact Us | Advertise with Us | Facebook | Blog | Recommend This Page




Copyright © 1998-2015 Mrs. Glosser's Math Goodies. All Rights Reserved.

A Hotchalk/Glam Partner Site - Last Modified 25 Jan 2015