Geometric Sequence Calculator

Your details

Forward mode: enter a, r, n. Reverse modes: solve for r, a, or n from other knowns.
The starting value of the sequence.
The fixed multiplier between consecutive terms. Cannot be 0.
Which term to find, counting from 1.
Start position for the partial-sum window. Leave at 1 for the standard Sₙ.
nth term (aₙ)Diverging, terms grow without bound
162
Sum of first n terms (Sₙ)242
Partial sum (term m to n)242
Common ratio (r)3
nth term162
Sum to n242
Partial sum242

The nth term is 162.

  • Each term is 3x the one before it, so the sequence grows geometrically.
  • The running sum of the first n terms is 242.
  • Because |r| >= 1, the infinite series has no finite sum; only a finite count of terms can be added.

Next stepChange n to jump to any other position, set |r| below 1 to model decay, or switch to Reverse Solve to find r from two known terms.

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