Geometric Sequence Calculator
nth term, sum of n terms, and the infinite sum when the ratio allows one.
The formulas
aₙ = a₁ · rⁿ⁻¹ Sₙ = a₁(rⁿ - 1)/(r - 1)
Each term is the previous times r. Starting at 3 with ratio 2: the 10th term is 3·2⁹ = 1,536 and the first ten sum to 3,069.
The infinite sum
When |r| < 1 the terms shrink toward zero and the whole infinite series converges to a₁/(1 - r). That's how 0.999... = 9/10 + 9/100 + ... sums exactly to 1, and why a bouncing ball covering half the remaining distance each time still travels a finite total.