Question
Rewrite each sequence of Table 1 in your notebook, along with the next three numbers in each sequences! After each sequences, write in your own words what is the rule for forming the numbers in the sequence.
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Answer
• All 1's 1, 1, 1, 1, ... (The next three numbers are 1, 1, 1. The rule is that every number is 1.)
• Counting numbers 1, 2, 3, 4, 5, 6, 7, ... (The next three numbers are 8, 9, 10. The rule is to add 1 to the previous number.)
• Odd numbers 1, 3, 5, 7, 9, 1,... (The next three numbers are 15, 17, 19. The rs to add 2 to the previous number.)n numbers 2, 4, 6, 8, 10, 12, 14, ... (The next three is to add 2 to the previous number.)
• Triangular numbers 1, 3, 6, 10, 15, 21, 28, ... (The next three numbers are 36, 45, 55. The rule is to add the next natural number is sequence.)
• Squares 1, 4, 9, 16, 25, 36, 49, ... (The next three numbers are 64, 81, 100. The rule is to square the next natural number.)
• Cubes 1, 8, 27, 64, 125, 216, ... (The next three numbers are 343, 512, 729. The rule is to cube the next natural number.)
• Virahanka numbers 1, 2, 3, 5, 8, 13, 21, ... (The next three numbers are 34, 55, 89. The rule is to add the last two numbers.)
• Powers of 2 1, 2, 4, 8, 16, 32, 64, ... (The next three numbers are 128, 256, 512. The rule is to multiply the last number by 2.)
• Powers of 3 1, 3, 9, 27, 81, 243, 729, ... (The next three numbers are 2187, 6561, 19683. The rule is to multiply the last number by 3.)
• Counting numbers 1, 2, 3, 4, 5, 6, 7, ... (The next three numbers are 8, 9, 10. The rule is to add 1 to the previous number.)
• Odd numbers 1, 3, 5, 7, 9, 1,... (The next three numbers are 15, 17, 19. The rs to add 2 to the previous number.)n numbers 2, 4, 6, 8, 10, 12, 14, ... (The next three is to add 2 to the previous number.)
• Triangular numbers 1, 3, 6, 10, 15, 21, 28, ... (The next three numbers are 36, 45, 55. The rule is to add the next natural number is sequence.)
• Squares 1, 4, 9, 16, 25, 36, 49, ... (The next three numbers are 64, 81, 100. The rule is to square the next natural number.)
• Cubes 1, 8, 27, 64, 125, 216, ... (The next three numbers are 343, 512, 729. The rule is to cube the next natural number.)
• Virahanka numbers 1, 2, 3, 5, 8, 13, 21, ... (The next three numbers are 34, 55, 89. The rule is to add the last two numbers.)
• Powers of 2 1, 2, 4, 8, 16, 32, 64, ... (The next three numbers are 128, 256, 512. The rule is to multiply the last number by 2.)
• Powers of 3 1, 3, 9, 27, 81, 243, 729, ... (The next three numbers are 2187, 6561, 19683. The rule is to multiply the last number by 3.)
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