The nth odd number is given by the formula 2n - 1.
This formula arises from the pattern of odd numbers. Odd numbers are integers that, when divided by 2, leave a remainder of 1. The sequence of odd numbers begins 1, 3, 5, 7, 9, and so on.
Here's how the formula works:
- n = 1: 2 * 1 - 1 = 1 (The first odd number)
- n = 2: 2 * 2 - 1 = 3 (The second odd number)
- n = 3: 2 * 3 - 1 = 5 (The third odd number)
- n = 4: 2 * 4 - 1 = 7 (The fourth odd number)
- n = 5: 2 * 5 - 1 = 9 (The fifth odd number)
The reference explicitly states, "The nth odd number is given by the formula 2*n-1."
| n | nth Odd Number |
|---|---|
| 1 | 1 |
| 2 | 3 |
| 3 | 5 |
| 4 | 7 |
| 5 | 9 |
| 6 | 11 |
| 7 | 13 |
| 8 | 15 |
Therefore, to find any odd number in the sequence, you simply substitute the desired position (n) into the formula 2n - 1.
