c) Complete the table of values.
| Term number | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Term value | | | | | | |
d) Describe the pattern in words.
e) Describe in words how the number of tiles in each term is related to the term number.
Answer (2)
The values in the table are completed based on an increasing pattern of tiles starting with 1 tile for term 0 and increasing by 2 tiles for each term. The completed table shows values of 1, 3, 5, 7, 9, and 11 for terms 0 through 5. The formula describing the relationship is Number of tiles = 2 × ( Term number ) + 1 .
;
The table of values is completed based on the assumption that the pattern starts with 1 tile for term 0 and increases by 2 for each subsequent term.
The pattern is described as the number of tiles increasing by 2 with each successive term.
The relationship between the number of tiles and the term number is described as: Number of tiles = 2 * (Term number) + 1.
The completed table is:
Term number
0
1
2
3
4
5
Term value
1
3
5
7
9
11
The relationship between the term number and term value is: 2 n + 1 , where n is the term number.
Explanation
Understanding the Problem The problem requires completing a table of values, describing a pattern, and explaining the relationship between the number of tiles and the term number. Since the visual representation of the pattern is missing, I will create an example pattern to illustrate the solution process. Let's assume the pattern is that the number of tiles increases by 2 with each term, starting with 1 tile for term number 0.
Calculating Term Values Based on the assumption that the pattern starts with 1 tile for term 0 and increases by 2 for each subsequent term, I can calculate the term values for term numbers 0 to 5.
Determining the Number of Tiles for Each Term Term 0: 1 tile Term 1: 1 + 2 = 3 tiles Term 2: 3 + 2 = 5 tiles Term 3: 5 + 2 = 7 tiles Term 4: 7 + 2 = 9 tiles Term 5: 9 + 2 = 11 tiles
Completing the Table of Values Now I can complete the table of values:
Term number
0
1
2
3
4
5
Term value
1
3
5
7
9
11
Describing the Pattern in Words The pattern is that the number of tiles increases by 2 with each successive term.
Describing the Relationship Between Tiles and Term Number The number of tiles in each term is equal to two times the term number, plus one. This can be expressed as: Number of tiles = 2 * (Term number) + 1.
Examples
Patterns like this are found everywhere! Imagine you're stacking cups. If you start with one cup and add two more to each level, the number of cups you have at each level follows this pattern. Understanding these patterns helps predict how many cups you'll need for a certain number of levels, which is useful for planning events or organizing storage.
