Sequence Sum Calculator

Calculator

Sequence Type

Start Index

End Index

Decimal Precision

First Term (a₁)

Common Difference (d)

First Term (a₁)

Common Ratio (r)

Custom Term Expression in n

Allowed examples: n, n*n+1, 2*n+3, sin(n), sqrt(n), pow(n,2).

Rows to Show in Table

Example Data Table

Sequence Type	Inputs	Range	Result
Arithmetic	a₁ = 3, d = 4	n = 1 to 5	3 + 7 + 11 + 15 + 19 = 55
Geometric	a₁ = 2, r = 3	n = 1 to 4	2 + 6 + 18 + 54 = 80
Custom	aₙ = n² + 1	n = 1 to 4	2 + 5 + 10 + 17 = 34

Formula Used

Arithmetic sequence: The nth term is aₙ = a₁ + (n - 1)d. For a selected range, the sum equals count × (first selected term + last selected term) / 2.

Geometric sequence: The nth term is aₙ = a₁r^(n - 1). This calculator evaluates the chosen range directly, which works for any positive starting index and for ratios including negative or fractional values.

Custom expression: The calculator computes each term from your expression in n, then adds the terms numerically across the selected index range using S = Σ aₙ.

How to Use This Calculator

Select arithmetic, geometric, or custom expression mode.
Enter the start and end indexes for the terms you want.
Provide the sequence parameters, such as first term and difference or ratio.
For custom mode, type an expression using n.
Set your preferred decimal precision and table size.
Click the calculate button to show the result above the form.
Review the summary, chart, and term-by-term table.
Download the result as CSV or PDF when needed.

FAQs

1. What does this calculator add together?

It adds the selected terms of a sequence between your chosen start and end indexes. You can work with arithmetic, geometric, or custom formula-based sequences.

2. Can I sum only part of a sequence?

Yes. Enter any positive start and end indexes. The calculator will sum only that chosen interval instead of forcing you to begin at the first term.

3. What is the difference between arithmetic and geometric sequences?

Arithmetic sequences change by a constant difference. Geometric sequences change by a constant ratio. One grows linearly, while the other can grow or decay exponentially.

4. How does custom expression mode work?

You enter a formula in n, such as n*n+1 or sin(n). The calculator evaluates each term in the selected range and then computes the running total.

5. Why does the chart show both term values and cumulative sums?

The term line shows how each individual value changes. The cumulative line shows how the total builds over time, which helps you see growth patterns quickly.

6. Can I use negative or fractional values?

Yes. Negative first terms, differences, ratios, and many fractional values work correctly. Very large magnitudes may overflow, so keep inputs within a practical numeric range.

7. What do the CSV and PDF exports include?

They include the summary values and the visible table rows. This makes it easier to share sequence results, archive computations, or compare multiple scenarios later.

8. Is this useful for classroom and exam practice?

Yes. It helps verify manual calculations, inspect patterns, and understand how changing parameters affects sums. It is especially useful for checking partial sums and finite series behavior.