Rule Form Arithmetic
Observe the following number pattern: 3, 6, 9, 12, 15, …
To find the nth term in the given pattern, we organize the sequence in a table:
| Number | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 |
|---|---|---|---|---|---|---|---|---|---|---|
| Pattern | 3×1 | 3×2 | 3×3 | 3×4 | 3×5 | … | 3×7 | … | 3×9 | … |
From the table, it is clear that the first number is 3 × 1, the second number is 3 × 2, and so on. Following this pattern, we can determine the nth term for any position in the sequence.
Thus, the general formula for the nth term of the pattern 3,
So, for any given n, the corresponding term in the pattern is 3 × n.