Graph
Example Data Table
| Mode | Input | Sequence | Sum |
|---|---|---|---|
| Sum and Count | 45, 5 | 7, 8, 9, 10, 11 | 45 |
| Start and Count | 4, 6 | 4, 5, 6, 7, 8, 9 | 39 |
| Range | 10 to 14 | 10, 11, 12, 13, 14 | 60 |
Formula Used
For n consecutive positive integers starting at a, the sequence is:
a, a + 1, a + 2, ... , a + n - 1
The sum is:
S = n / 2 × [2a + (n - 1)]
When sum and count are known:
a = [S - n(n - 1) / 2] / n
How to Use This Calculator
Select the calculation mode first. Use sum and count when you know the total and number of terms. Use start and count when you want to create a sequence from a first number. Use range when you know both endpoints. Press calculate. The result appears above the form.
Understanding Consecutive Positive Integers
What They Mean
Consecutive positive integers are counting numbers placed in direct order. Each number is one greater than the previous number. Examples include 1, 2, 3 and 12, 13, 14. They are simple, but they appear in many algebra questions.
Why This Calculator Helps
This calculator reduces manual trial and error. You can find a hidden sequence from a given sum. You can also build a sequence from a starting number. It checks whether the first term is positive and whole. This prevents invalid answers.
Common Learning Use
Students often solve word problems about unknown integers. A question may say that five consecutive positive integers have a sum of 80. The calculator uses the arithmetic sequence formula. It then returns the first number and all following terms.
Advanced Options
The tool supports three useful modes. Sum and count mode solves unknown sequences. Start and count mode creates custom lists. Range mode studies all positive integers between two values. The output includes total, average, first value, and last value.
Checking Results
Always check the sum after calculation. The listed sequence should add to the target value. If no exact sequence exists, the calculator shows a warning. That means the sum cannot be split into the selected count of consecutive positive integers.
Practical Benefits
The chart helps compare term growth. The CSV file saves the result for spreadsheets. The PDF file creates a quick report. These features are useful for homework, teaching notes, examples, and simple number pattern analysis.
FAQs
What are consecutive positive integers?
They are whole numbers greater than zero, listed without gaps. Each next number increases by one.
Can the calculator find missing integers from a sum?
Yes. Choose sum and count mode. Enter the total sum and number of required integers.
Why does it show no exact sequence?
The calculated first term may be decimal, zero, or negative. Then no valid positive integer sequence exists.
Does the sequence always increase by one?
Yes. Consecutive positive integers always use a fixed step of one between neighboring terms.
Can I calculate only a range?
Yes. Select range mode. Enter starting and ending positive integers to build the list.
What does the average mean?
The average is the sum divided by count. It is also the middle value for odd counts.
Can I download results?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a simple report.
Is this useful for algebra problems?
Yes. It helps solve number pattern questions and checks arithmetic sequence work quickly.