A geometric sequence multiplies by a constant ratio. Example: 2, 6, 18, 54 (ratio = 3).
nth term: a_n = a₁ × r^(n-1). Sum of n terms: S_n = a₁ × (1 - r^n) / (1 - r)
Use this calculator whenever mental arithmetic introduces uncertainty — particularly when the result will inform a decision rather than just satisfy curiosity. Even confident mathematicians use calculation tools when precision matters.
The most frequent error is rounding intermediate values before completing the full calculation. Round only the final result — rounding intermediate steps compounds errors in multi-step calculations, sometimes significantly.
A business owner spots that revenue grew from £180,000 last year to £213,400 this year. The calculator confirms the increase is 18.6% — a figure needed for the annual report and for comparing against the industry growth rate cited in the sector report.
A sequence where each term is the previous term multiplied by a constant ratio (r).
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