Question 2 - Patterns in Numbers - Chapter 1 Class 6 - Patterns in Mathematics (Ganit Prakash)

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Question 2 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.1, 1, 1, 1, 1, 1, 1, ... 1, 2, 3, 4, 5, 6, 7, ... 1, 3, 5, 7, 9, 11, 13, ... 2, 4, 6, 8, 10, 12, 14, ... 1, 3, 6, 10, 15, 21, 28, ... 1, 4, 9, 16, 25, 36, 49, ... 1, 8, 27, 64, 125, 216, ... 1, 2, 3, 5, 8, 13, 21, ... 1, 2, 4, 8, 16, 32, 64, ... 1, 3, 9, 27, 81, 243, 729, ... 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,... 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, ... 2, 4, 6, 8, 10, 12, 14, 16, 18, 20,... 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,... 1, 4, 9, 16, 25, 36, 49, 64, 81, 100,... 1, 8, 27, 64, 125, 216, 343, 512, 729... 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 ... 1, 2, 4, 8, 16, 32, 64, 128, 256, 512... 1, 3, 9, 27, 81, 243, 729, 2187,6561, 19683... Sequence: 1, 1, 1, 1, 1, 1, ... Pattern: Every number is just 1. Next 3 numbers are 1, 1, 1 So, new sequence is 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 2. Sequence: 1, 2, 3, 4, 5, 6, ... Pattern: We add by 1 each time. Next 3 numbers are 6 + 1 = 7, 7 + 1 = 8, 8 + 1 = 9 9 × 9 = 64, 10 × 10 = 100, So, new sequence is 1, 4, 9, 16, 25, 36, 49, 64, 81, 100,... 7. Sequence: 1, 8, 27, 64, 125, 216, ... Pattern: Multiply a number by itself thrice: 1 × 1 × 1, 2 × 2 × 2 , 3 × 3 × 3 ... Next 3 numbers are 7 × 7 × 7 = 343, 8 × 8 × 8 = 512, 9 × 9 × 9 = 729, So, new sequence is 1, 8, 27, 64, 125, 216, 343, 512, 729... So, new sequence is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,... 3. Sequence: 1, 3, 5, 7, 9, 11, ... Pattern: We add by 2 each time, and all numbers are odd Next 3 numbers are 11 + 2 = 13, 9. Sequence: 1, 2, 4, 8, 16, 32, 64, ... Pattern: This seems like Multiply by 2 each time. Next 3 numbers are 64 × 2 = 128, 128 × 2 = 256, 256 × 2 = 512, So, new sequence is 1, 2, 4, 8, 16, 32, 64, 128, 256, 512... 10. Sequence: 1, 3, 9, 27, 81, 243, 729... Pattern: This seems like Multiply by 3 each time. Next 3 numbers are 729 × 3 = 2,187 , 2187 × 3 = 6,561 , 6561 × 3 = 19,683 , So, new sequence is 1, 3, 9, 27, 81, 243, 729, 2187,6561, 19683... 13 + 2 = 15, 15 + 2 = 17 So, new sequence is 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, ... 4. Sequence: 2, 4, 6, 8, 10, 12, 14, ... Pattern: We add by 2 each time, and all numbers are even Next 3 numbers are 12 + 2 = 14, 14 + 2 = 16, 16 + 2 = 18 5. Sequence: 1, 3, 6, 10, 15, 21, 28, ... Pattern: We add numbers like this: +2, +3, +4, +5, +6... Next 3 numbers are 28 + 8 = 36, 36 + 9 = 45, 45 + 10 = 55 So, new sequence is 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,... 6. Sequence: 1, 4, 9, 16, 25, 36, 49... Pattern: Multiply a number by itself: 1 × 1, 2 × 2, 3 × 3, 4 × 4... Next 3 numbers are 8 × 8 = 64,