Geometric Series Sum
Worked example: 3 + 6 + ... + 384 (8 terms) → S = 765 — press Try an example to run it live, then adjust anything.
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Grade 11Grade 11 Math — Functions & Applications
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Geometric Series Sum explained
Adding the first n terms of a geometric sequence collapses to a single fraction: a₁(1 − rⁿ)/(1 − r). The legendary chessboard reward — 1 grain of wheat on the first square, doubling each square — sums to (2⁶⁴ − 1) ≈ 1.8 × 10¹⁹ grains over 64 squares, more wheat than the world has ever grown.
Shrinking ratios are just as practical: saving $100 in month one but only 80% as much each following month accumulates S = 100(1 − 0.8¹²)/(1 − 0.8) ≈ $465.64 over a year, already close to the $500 ceiling the infinite series would give.
Geometric Series Sum formula
- = Sum of the first n terms
- = First term
- = Common ratio
- = Number of terms
Missing one of these? Work it out first, then come back
- Sum of the first n terms — Arithmetic Series Sum
- First term — Arithmetic Sequence nth Term, Arithmetic Series Sum
- Common ratio — Geometric Sequence nth Term, Infinite Geometric Series
- Number of terms — Exponential Growth, Exponential Decay