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

Transcript

Question 1 Can you recognise the pattern in each of the sequences in Table 1?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, ... Sequence: 1, 1, 1, 1, 1, 1, ... Pattern: Every number is just 1. Therefore, pattern is All 1’s 2. Sequence: 1, 2, 3, 4, 5, 6, ... Pattern: We add by 1 each time. Therefore, pattern is Counting numbers 3. Sequence: 1, 3, 5, 7, 9, 11, ... Pattern: We add by 2 each time, and all numbers are odd Therefore, pattern is Odd Numbers 4. Sequence: 2, 4, 6, 8, 10, 12, ... Pattern: We add by 2 each time, and all numbers are even Therefore, pattern is Even Numbers 5. Sequence: 1, 3, 6, 10, 15, 21, ... Pattern: We add numbers like this: +2, +3, +4, +5, +6... These are called triangular numbers Therefore, pattern is Triangular Numbers 6. Sequence: 1, 4, 9, 16, 25, 36, ... Pattern: Multiply a number by itself: 1 × 1, 2 × 2, 3 × 3, 4 × 4... Therefore, pattern is Square Numbers 7. Sequence: 1, 8, 27, 64, 125, ... Pattern: Multiply a number by itself thrice: 1 × 1 × 1, 2 × 2 × 2 , 3 × 3 × 3 ... Therefore, pattern is Cube Numbers 8. Sequence: 1, 2, 3, 5, 8, 13, 21, ... This is similar to Fibonacci Pattern: Each number = Sum of previous two numbers Like 3 = 2 + 1, 5 = 3 + 2 8 = 5 + 2 Therefore, pattern is Virahānka Numbers (Like Fibonacci) 9. Sequence: 1, 2, 4, 8, 16, 32, 64, ... Pattern: This seems like Multiply by 2 each time. Like 2 = 1 × 2 4 = 2 × 2 8 = 4 × 2 16 = 8 × 2 Therefore, pattern is Powers of 2 10. Sequence: 1, 3, 9, 27, 81, 243, ... Pattern: This seems like Multiply by 3 each time. Like 3 = 1 × 3 9 = 3 × 3 27 = 9 × 3 81 = 27 × 3 Therefore, pattern is Powers of 3 The completed pattern is 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, ... (All 1’s) (Counting numbers) (Odd numbers) (Even numbers) (Triangular numbers) (Squares) (Cubes) (Virahānka numbers) (Powers of 2) (Powers of 3)