Solution: Figure It Out 1.2

Section 1.2: Patterns in Numbers

Q1. Can you recognise the pattern in each of the sequences in Table 1?

Answer: Yes, here are the patterns:

• Powers of 2: $1, 2, 4, 8, 16 \dots$ (Multiply previous number by 2).
• Powers of 3: $1, 3, 9, 27, 81 \dots$ (Multiply previous number by 3).
• Virahanka Numbers: $1, 2, 3, 5, 8 \dots$ (Add the previous two numbers: $1+2=3, 2+3=5$).

Q2. Rewrite each sequence of Table 1 in your notebook, along with the next three numbers.

Answer:

1. All 1’s: $1, 1, 1, \dots$ Next: 1, 1, 1 (Rule: Constant 1).
2. Counting: $1, 2, 3, 4, 5, 6, 7, \dots$ Next: 8, 9, 10 (Rule: Add 1).
3. Odd: $1, 3, 5, 7, 9, 11, 13, \dots$ Next: 15, 17, 19 (Rule: Add 2).
4. Even: $2, 4, 6, 8, 10, 12, 14, \dots$ Next: 16, 18, 20 (Rule: Add 2).
5. Triangular: $1, 3, 6, 10, 15, 21, 28, \dots$ Next: 36, 45, 55 (Rule: Add increasing counting numbers $+8, +9, +10$).
6. Squares: $1, 4, 9, 16, 25, 36, 49, \dots$ Next: 64, 81, 100 (Rule: $8^2, 9^2, 10^2$).
7. Cubes: $1, 8, 27, 64, 125, 216, \dots$ Next: 343, 512, 729 (Rule: $7^3, 8^3, 9^3$).