Extending Sequences in Table 1: 1. All 1’s Sequence: The next three numbers are 1, 1, 1. The rule is that every number in the sequence is 1. 2. Counting Numbers Sequence: The next three numbers are 8, 9, 10. The rule is to add 1 to the previous number. 3.Odd Numbers Sequence: The next three numbersRead more
Extending Sequences in Table 1:
1. All 1’s Sequence: The next three numbers are 1, 1, 1. The rule is that every number in the sequence is 1.
2. Counting Numbers Sequence: The next three numbers are 8, 9, 10. The rule is to add 1 to the previous number.
3.Odd Numbers Sequence: The next three numbers are 15, 17, 19. The rule is to add 2 to the previous number.
4. Even Numbers Sequence: The next three numbers are 16, 18, 20. The rule is to add 2 to the previous number.
5. Triangular Numbers Sequence: The next three numbers are 36, 45, 55. The rule is to add the next counting number to the previous triangular number (e.g., 1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10, …).
6. Squares Sequence: The next three numbers are 64, 81, 100. The rule is to square the next counting number (e.g., 8² = 64, 9² = 81, 10² = 100).
7.Cubes Sequence: The next three numbers are 125, 216, 343. The rule is to cube the next counting number (e.g., 5³ = 125, 6³ = 216, 7³ = 343).
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.
Rewrite each sequence of Table 1 in your notebook, along with the next three numbers in each sequence! After each sequence, write in your own words what is the rule for forming the numbers in the sequence.
Extending Sequences in Table 1: 1. All 1’s Sequence: The next three numbers are 1, 1, 1. The rule is that every number in the sequence is 1. 2. Counting Numbers Sequence: The next three numbers are 8, 9, 10. The rule is to add 1 to the previous number. 3.Odd Numbers Sequence: The next three numbersRead more
Extending Sequences in Table 1:
See less1. All 1’s Sequence: The next three numbers are 1, 1, 1. The rule is that every number in the sequence is 1.
2. Counting Numbers Sequence: The next three numbers are 8, 9, 10. The rule is to add 1 to the previous number.
3.Odd Numbers Sequence: The next three numbers are 15, 17, 19. The rule is to add 2 to the previous number.
4. Even Numbers Sequence: The next three numbers are 16, 18, 20. The rule is to add 2 to the previous number.
5. Triangular Numbers Sequence: The next three numbers are 36, 45, 55. The rule is to add the next counting number to the previous triangular number (e.g., 1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10, …).
6. Squares Sequence: The next three numbers are 64, 81, 100. The rule is to square the next counting number (e.g., 8² = 64, 9² = 81, 10² = 100).
7.Cubes Sequence: The next three numbers are 125, 216, 343. The rule is to cube the next counting number (e.g., 5³ = 125, 6³ = 216, 7³ = 343).
Copy the pictorial representations of the number sequences in Table 2 in your notebook, and draw the next picture for each sequence!
The pictorial representations of the number sequences:
The pictorial representations of the number sequences:
See lessWhy 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