Calculator
Example Data Table
| First Term | Common Difference | Number of Terms | Last Term | Sum |
|---|---|---|---|---|
| 2 | 3 | 5 | 14 | 40 |
| 7 | 2 | 8 | 21 | 112 |
| 10 | -1 | 6 | 5 | 45 |
| 4 | 4 | 7 | 28 | 112 |
Formula Used
Using first term, common difference, and number of terms:
Sn = n / 2 × [2a + (n − 1)d]
Using first term, last term, and number of terms:
Sn = n(a + l) / 2
Last term formula:
l = a + (n − 1)d
Common difference from first and last terms:
d = (l − a) / (n − 1)
How to Use This Calculator
- Select your preferred input mode.
- Enter the first term.
- Enter either the common difference or the last term.
- Enter the total number of terms.
- Click the calculate button.
- Review the sum, nth term, average, and sequence preview.
- Download the output as CSV or PDF if needed.
About This Sum of Finite Arithmetic Sequence Calculator
What this calculator does
This sum of finite arithmetic sequence calculator helps you add terms in an arithmetic series fast. It works when each term changes by the same amount. You can solve school problems, check manual work, or review number patterns with less effort.
Why arithmetic sequences matter
Arithmetic sequences appear in many maths topics. They also show up in finance, coding logic, measurement tasks, and planning problems. Equal step changes make patterns easier to track. A strong calculator can save time and reduce small input mistakes.
Two flexible solving methods
This page gives you two ways to find the total. You can use the first term, common difference, and number of terms. You can also use the first term, last term, and number of terms. That flexibility helps with homework, revision, and classroom examples.
Useful outputs for better understanding
The calculator does more than return one value. It also shows the last or nth term, the average term value, and a short sequence preview. These extra details help you confirm that the pattern is correct before using the final sum in another step.
How the formula works
The standard arithmetic series sum formula uses the first term, difference, and total count of terms. Another version uses the first and last term. Both formulas lead to the same answer when the sequence is valid. This makes the tool useful for checking algebraic substitutions.
Good for learning and quick verification
Students often need a fast way to verify arithmetic progression questions. Teachers may want clear examples. Professionals may need quick totals from evenly spaced values. This calculator supports all three use cases with simple inputs and readable outputs.
Example situations
You can use it for staircase number patterns, weekly savings plans, equally spaced inventory counts, or score sequences. It is also helpful when building practice worksheets. The included example data table gives you quick reference values for common arithmetic sequence problems.
Export and reporting support
After calculation, you can download the result as CSV or PDF. That makes record keeping easier. It also supports notes, worksheets, and digital reports. When accuracy matters, exporting the results helps you reuse values without typing them again.
FAQs
1. What is a finite arithmetic sequence?
A finite arithmetic sequence is a list of numbers with a constant difference between consecutive terms and a fixed ending point after a certain number of terms.
2. What formula is used for the sum?
The calculator uses either Sn = n/2 × [2a + (n−1)d] or Sn = n(a + l)/2. The correct version depends on your input mode.
3. Can I use negative differences?
Yes. A negative common difference creates a decreasing arithmetic sequence. The calculator still finds the correct last term, average, and total sum.
4. Why does the calculator show the nth term?
The nth term helps confirm that your sequence is correct. It also lets you verify the final value before using the sum in another formula or worksheet.
5. What happens when the number of terms is one?
If there is only one term, the sum equals that single term. In first and last term mode, both values must match for the sequence to remain valid.
6. Is this calculator useful for students?
Yes. It is useful for algebra practice, arithmetic progression lessons, exam revision, and checking manual calculations with clear outputs and simple steps.
7. Can I download the result?
Yes. After calculating, you can download the result as a CSV file or a PDF file for records, reports, worksheets, or later review.
8. When should I use first and last term mode?
Use that mode when you already know the sequence start, the sequence end, and the number of terms. It gives a fast total without entering the difference separately.