Download Mathematics 3206 Name: Purpose Procedure 5th Square Number

Mathematics 3206
Name:______________________
Investigation #5 – Solving Problems Using Sequences of Differences (p 21) Section 1.3
Numbers that can be arranged in the shape of a square are called square numbers. The first four square
numbers and the number of dots used to form each square are shown below.
1st
2nd
3rd
4th
(1 dot)
(4 dots)
(9 dots)
(16 dots)
Purpose
Explore various ways that number patterns can grow, other than at a uniform or constant rate. Use
sequences of differences to solve problems.
Procedure
•
Determine the next two square numbers and draw them in the table below.
5th Square Number
•
•
Write the number of dots in each square as terms of a sequence.
{ ___,
Complete the table below.
First Level
Difference,
D1
Second
Level
Difference,
D2
•
6th Square Number
___, ___, ___, ___, ___ …
Sequence
{ ___,
___, ___, ___, ___, …
{ ___,
What do you notice about each term in D2?
___, ___, ___, …
}
}
}
Questions
1.
How do you know that the sequence determined from the square numbers is not an arithmetic
sequence?
2. Graph below the number of dots in each square number versus the term number.
Number of Dots
Number of Dots in Square Number
40
35
30
25
20
Describe the shape of the
graph to the left.
15
10
5
0
1
2
3
4
5
6
7
8
Term Number
3. How is the graph in #2 different from the graph of an arithmetic sequence?
4. Determine a rule or relation that will generate the sequence from the square numbers.
Let tn = number of dots and n = the term number.
5. Use the relation or rule to determine the number of dots in the 50th square number.
6. How do you know that the relation or rule used in #4 is a relation or rule?