How to use this calculator
Choose arithmetic, geometric, or recurrence, then enter first term, difference/ratio, and n.
Formula and method
Arithmetic aₙ=a₁+(n−1)d, Sₙ=n(a₁+aₙ)/2. Geometric aₙ=a₁rⁿ⁻¹; Sₙ=a₁(1−rⁿ)/(1−r) for r≠1.
Worked example
Arithmetic a₁=2, d=3, n=6 gives a₆=17 and sum 57.
Assumptions and supported scope
Finite sequences of 1–100 terms. Recurrence supports only aₙ=p aₙ₋₁+q. Floating-point values can accumulate rounding error; infinite series tests are outside scope.
Method references
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