Q1.
Can you recognise the pattern in each of the sequences in Table 1?
Table 1 of the chapter — ten number sequences with their names.
| 1, 1, 1, 1, 1, 1, 1, … | (All 1’s) |
| 1, 2, 3, 4, 5, 6, 7, … | (Counting numbers) |
| 1, 3, 5, 7, 9, 11, 13, … | (Odd numbers) |
| 2, 4, 6, 8, 10, 12, 14, … | (Even numbers) |
| 1, 3, 6, 10, 15, 21, 28, … | (Triangular numbers) |
| 1, 4, 9, 16, 25, 36, 49, … | (Squares) |
| 1, 8, 27, 64, 125, 216, … | (Cubes) |
| 1, 2, 3, 5, 8, 13, 21, … | (Virahānka numbers) |
| 1, 2, 4, 8, 16, 32, 64, … | (Powers of 2) |
| 1, 3, 9, 27, 81, 243, 729, … | (Powers of 3) |
Answer
Yes. Each sequence in Table 1 is built by one simple rule, repeated again and again:
- All 1's — the same number 1 is written every time.
- Counting numbers — add 1 to the previous number.
- Odd numbers — start at 1 and keep adding 2.
- Even numbers — start at 2 and keep adding 2.
- Triangular numbers — add 2, then 3, then 4, then 5, … (the amount added grows by one each time).
- Squares — multiply a counting number by itself: 1×1, 2×2, 3×3, …
- Cubes — multiply a counting number by itself three times: 1×1×1, 2×2×2, 3×3×3, …
- Virahānka numbers — each number is the sum of the two numbers before it (2+3 = 5, 3+5 = 8, 5+8 = 13).
- Powers of 2 — double the previous number.
- Powers of 3 — multiply the previous number by 3.
Why it matters: once you can say the rule in words, you can continue the sequence as far as you like — you no longer need to remember the numbers.