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Geometric Patterns: Constant Difference

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Questions and Answers

What is the number of hexagons in the 8th figure?

9
6
8 (correct)
7

What is the common rule for the pattern of triangles?

No. of triangles = FN - 1
No. of triangles = FN × 2
No. of triangles = FN (correct)
No. of triangles = FN + 1

How many circles are in the 15th figure?

14
13
16
15 (correct)

What is the difference between the patterns in questions about circles and starting with 2 circles?

The second pattern starts with 2 circles and increases. (D) Signup and view all the answers

What is the rule for the number of cubes in the pattern?

No. of cubes = Figure number + 1 (A) Signup and view all the answers

How many cubes are in the 11th figure?

12 (A) Signup and view all the answers

What is the number of hexagons in the 8th figure?

8 (A) Signup and view all the answers

What is the rule for determining the number of triangles in each figure?

No. of triangles = Figure number (A) Signup and view all the answers

How many circles are in the 15th figure?

15 (C) Signup and view all the answers

What is the starting number of circles in the extended pattern?

2 (B) Signup and view all the answers

Using the extended pattern, what is the number of circles in the 4th figure?

5 (D) Signup and view all the answers

If the figure number is 18, how many cubes are there?

19 (D) Signup and view all the answers

How many hexagons are in the 11th figure?

11 (A) Signup and view all the answers

What is the rule for the number of circles in question 4?

No. of circles = Figure number (D) Signup and view all the answers

What is the rule for the number of cubes?

No. of cubes = Figure number + 1 (C) Signup and view all the answers

What is the common feature in the patterns for hexagons, triangles, and circles in question 3?

The number of shapes equals the figure number (A) Signup and view all the answers

How does the pattern in question 5 start differently from question 4?

It starts with 2 circles (C) Signup and view all the answers

What is the number of triangles in the 10th figure?

10 (C) Signup and view all the answers

Study Notes

Geometric Patterns

Patterns with a Constant Difference of 1

A "constant difference" means that the same number of shapes/objects are added to each new figure in a pattern.
In these questions, the constant difference is 1.

Hexagons Pattern

The rule for the number of hexagons is: No.of hexagons = Figure number
| Figure number | No.of hexagons | | 1 | 1 | | 2 | 2 | | 3 | 3 | | 4 | 4 | | 5 | 5 | | 8 | 8 | | 11 | 11 |

Triangles Pattern

The rule for the number of triangles is: No.of triangles = FN
| Figure number | No.of triangles | | 1 | 1 | | 2 | 2 | | 3 | 3 | | 5 | 5 | | 7 | 7 | | 10 | 10 |

Circles Pattern

The rule for the number of circles is: No.of circles = FN
| Figure number | No.of circles | | 1 | 1 | | 2 | 2 | | 3 | 3 | | 4 | 4 | | 5 | 5 | | 15 | 15 |

Different Circles Pattern

This pattern starts with 2.
The rule for the number of circles is: No.of circles = +1
| Figure number | Number of circles | | 1 | 2 | | 2 | 3 | | 3 | 4 | | 4 | 5 | | 5 | 6 | | 15 | 16 |

Cubes Pattern

The rule for the number of cubes is: No.of cubes = +1
| Figure number | Number of cubes | | 1 | 2 | | 2 | 3 | | 3 | 4 | | 4 | 5 | | 11 | 12 | | 18 | 19 |

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Description

Learn about geometric patterns with a constant difference of 1. Identify and apply the rule to complete the table and draw the 4th figure in the pattern.