The first odd integer sum is 1.
Based on the provided reference, "The total of any set of sequential odd numbers beginning with 1 is always equal to the square of the number of digits, added together. If 1,3,5,7,9,11,…, (2n-1) are the odd numbers, then; Sum of first odd number = 1". This clearly indicates that when considering only the first odd number in the sequence (which is 1 itself), the sum is 1.
To further clarify, consider the sequence of odd numbers:
1, 3, 5, 7, 9, 11...
- The sum of the first 1 odd number (1) is 1.
- The sum of the first 2 odd numbers (1+3) is 4 (which is 22).
- The sum of the first 3 odd numbers (1+3+5) is 9 (which is 32).
- The sum of the first 4 odd numbers (1+3+5+7) is 16 (which is 42).
This pattern continues to hold true, but for the specific question, we're only interested in the first odd number sum, which is the first odd number itself.
Therefore:
- First Odd Number: 1
- First Odd Integer Sum: 1
| Number of Odd Integers | Odd Integers | Sum |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 1, 3 | 4 |
| 3 | 1, 3, 5 | 9 |
| 4 | 1, 3, 5, 7 | 16 |
| 5 | 1, 3, 5, 7, 9 | 25 |
| n | 1, 3, 5, ..., (2n-1) | n2 |
The table shows that the sum of the first 'n' odd integers is equal to n2.
