Recognising the Patterns in Sequences: 1. All 1's Sequence (1, 1, 1, 1, ...): Each number in the sequence is always 1. 2. Counting Numbers (1, 2, 3, 4, ...): Each number increases by 1. 3. Odd Numbers (1, 3, 5, 7, ...): Each number increases by 2, starting from 1. 4. Even Numbers (2, 4, 6, 8, ...):Read more
Recognising the Patterns in Sequences:
1. All 1’s Sequence (1, 1, 1, 1, …): Each number in the sequence is always 1.
2. Counting Numbers (1, 2, 3, 4, …): Each number increases by 1.
3. Odd Numbers (1, 3, 5, 7, …): Each number increases by 2, starting from 1.
4. Even Numbers (2, 4, 6, 8, …): Each number increases by 2, starting from 2.
5. Triangular Numbers (1, 3, 6, 10, …): The difference between consecutive numbers increases by 1 each time.
6. Squares (1, 4, 9, 16, …): Each number is the square of a natural number (e.g., 1², 2², 3², …).
7. Cubes (1, 8, 27, 64, …): Each number is the cube of a natural number (e.g., 1³, 2³, 3³, …).
Triangular numbers (1, 3, 6, 10, 15, …) are called so because they can be represented by dots arranged in the shape of a triangle. For example, 3 dots form a triangle with two at the bottom and one at the top. Square numbers (1, 4, 9, 16, 25, …) are called squares because they can be arranged in a sRead more
Triangular numbers (1, 3, 6, 10, 15, …) are called so because they can be represented by dots arranged in the shape of a triangle. For example, 3 dots form a triangle with two at the bottom and one at the top. Square numbers (1, 4, 9, 16, 25, …) are called squares because they can be arranged in a square grid, like 4 dots forming a 2 x 2 square. Cubes (1, 8, 27, 64, 125, …) represent the number of small cubes that fit into a larger cube, with each number being the cube of an integer, like 3 x 3 x 3 for 27.
Can you recognize the pattern in each of the sequences in Table 1?
Recognising the Patterns in Sequences: 1. All 1's Sequence (1, 1, 1, 1, ...): Each number in the sequence is always 1. 2. Counting Numbers (1, 2, 3, 4, ...): Each number increases by 1. 3. Odd Numbers (1, 3, 5, 7, ...): Each number increases by 2, starting from 1. 4. Even Numbers (2, 4, 6, 8, ...):Read more
Recognising the Patterns in Sequences:
See less1. All 1’s Sequence (1, 1, 1, 1, …): Each number in the sequence is always 1.
2. Counting Numbers (1, 2, 3, 4, …): Each number increases by 1.
3. Odd Numbers (1, 3, 5, 7, …): Each number increases by 2, starting from 1.
4. Even Numbers (2, 4, 6, 8, …): Each number increases by 2, starting from 2.
5. Triangular Numbers (1, 3, 6, 10, …): The difference between consecutive numbers increases by 1 each time.
6. Squares (1, 4, 9, 16, …): Each number is the square of a natural number (e.g., 1², 2², 3², …).
7. Cubes (1, 8, 27, 64, …): Each number is the cube of a natural number (e.g., 1³, 2³, 3³, …).
Why are 1, 3, 6, 10, 15, … called triangular numbers? Why are 1, 4, 9, 16, 25, … called square numbers or squares? Why are 1, 8, 27, 64, 125, … called cubes?
Triangular numbers (1, 3, 6, 10, 15, …) are called so because they can be represented by dots arranged in the shape of a triangle. For example, 3 dots form a triangle with two at the bottom and one at the top. Square numbers (1, 4, 9, 16, 25, …) are called squares because they can be arranged in a sRead more
Triangular numbers (1, 3, 6, 10, 15, …) are called so because they can be represented by dots arranged in the shape of a triangle. For example, 3 dots form a triangle with two at the bottom and one at the top. Square numbers (1, 4, 9, 16, 25, …) are called squares because they can be arranged in a square grid, like 4 dots forming a 2 x 2 square. Cubes (1, 8, 27, 64, 125, …) represent the number of small cubes that fit into a larger cube, with each number being the cube of an integer, like 3 x 3 x 3 for 27.
See less