Comprehensive Calculator Guide
This calculator finds consecutive integers, or consecutive even or odd ones, that add up to a given total, with the equation solved as in textbooks. Five consecutive integers adding to 75 are 13 to 17; three consecutive even integers adding to 48 are 14, 16 and 18.
Solving
Let the smallest be x; consecutive numbers are x, x + 1, …, and even or odd ones x, x + 2, …. Sum, set equal to the total and solve. The average, total ÷ count, is the middle number when the count is odd. Some totals have no solution.
How to Use
- Enter the total.
- Enter how many numbers and their kind.
- Press “Find them” to see the numbers and the equation.
Formula Used
x = (S − d × n(n − 1)/2) ÷ n, d = 1 or 2
Practical Examples
- Example 1
- 75 from 5: 13 to 17.
- Example 2
- 48 from 3 even: 14, 16, 18.
Important Tips
- Start from the average.
- Even or odd: step 2.
- Add them to check.
Common Mistakes to Avoid
- Using x, x + 1 for even numbers.
- Forgetting odd numbers step by 2.
- Accepting a fractional x.
Frequently Asked Questions
- Three consecutive adding to 66?
- 21, 22, 23.
- Odd consecutive algebraically?
- x, x + 2, x + 4.
- Four consecutive adding to 75?
- None.