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Question
Tabulate and find the relationship between the variables (x and y) for the following patterns.
Solution
Let the number of steps be x and the number of shapes be y.
Tabulating the values of x and y
| Steps (x) | 1 | 2 | 3 | 4 | 5 |
| Shapes (y) | 1 | 3 | 5 | 7 | 9 |
From the table x = 1 ⇒ y = 1 = 1
x = 2 ⇒ y = 2 + 1 = 3
x = 3 ⇒ y = 3 + 2 = 5
x = 4 ⇒ y = 4 + 3 = 7
x = 5 ⇒ y = 5 + 4 = 9
Hence the relationship between x and y is y = 2x − 1.
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RELATED QUESTIONS
Match the given patterns of shapes with the appropriate number pattern and its generalization.
| Column A |
Column B |
|
| (i) |  |
(a) Sequence: 5, 9, 13, 17 ... General form: y = 4n + 1 |
| (ii) |  |
(b) Sequence: 3, 4, 5, 6, ...
General form: y = x + 2 |
| (iii) |  |
(c) Sequence: 1, 4, 9, 16 ...
General form: y = n2 |
| (iv) |  |
(d) Sequence: 2, 4, 6, 8 ...
General form: y = 2n |
| (v) |  |
(e) Sequence: 4, 16, 36, 64 ...
General form: y = 4n2 |
Identify the correct relationship between x andy from the given table.
| x | 1 | 2 | 3 | 4 | ... |
| y | 4 | 8 | 12 | 16 | ... |
Identify the correct relationship between x and y from the given table.
| x | −2 | −1 | 0 | 1 | 2 | ... |
| y | 6 | 3 | 0 | −3 | −6 | ... |
Choose the correct relationship between x and y from the given table.
| x | −2 | −1 | 0 | 1 | 2 | ... |
| y | 4 | 5 | 6 | 7 | 8 | ... |
Tabulate and find the relationship between the variables (x and y) for the following patterns.
