Sequence Calculator
Find the nth term and sum of an arithmetic or geometric sequence. Inspect terms, running totals, a term graph and a convergent geometric sum where applicable.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
An arithmetic sequence adds the same difference each time; a geometric sequence multiplies by the same ratio. The first term has index 1. The calculator sums the first n terms and shows the first 50 terms plus the exact requested index if larger.
Arithmetic: aₙ = a₁+(n−1)d; Sₙ = n(a₁+aₙ)/2. Geometric: aₙ = a₁rⁿ⁻¹; Sₙ = a₁(1−rⁿ)/(1−r), or na₁ when r=1.
Worked example
An arithmetic sequence starting at 3 with difference 2 has terms 3, 5, 7, …, 21. Its 10th term is 21 and its first 10 terms sum to 120. A geometric sequence starting at 3 with ratio 2 has 10th term 1536 and sum 3069.
Assumptions and input details
Use integer n from 1 to 10,000. Negative differences and ratios are allowed; a negative ratio may alternate signs. For |r| < 1 the infinite geometric sum a₁/(1−r) is also shown; otherwise it is not offered. For n > 50 the chart shows only the first 50 terms and the final term is listed separately in the table, with the gap disclosed. Results are floating-point approximations, bounded to absolute magnitude 1e100; underflowing nonzero geometric terms are rejected rather than silently displayed as zero.
References: OpenStax: sequences and series equations
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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