nth term (aₙ)
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Sum of n terms (Sₙ)
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Infinite sum (|r| < 1)
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Step by step
Find the nth term, the partial sum, and (when it converges) the infinite sum of a geometric sequence.
Step by step
Enter the first term, common ratio and term count.
a₁ is the first term, r is the constant factor each term is multiplied by, and n is how many terms.
aₙ = a₁·r⁽ⁿ⁻¹⁾ gives the nth term.
The partial sum uses Sₙ = a₁(rⁿ − 1) ⁄ (r − 1); the infinite sum a₁ ⁄ (1 − r) exists only when |r| < 1.