Algebra
Class 11

Geometric Progression - Sum of n Terms

Sn=arn1r1 (for r1)S_n = a \cdot \frac{r^n - 1}{r - 1} \text{ (for } r \neq 1)
2468101214020k40k60k80k100k
Sₙ = a(rⁿ-1)/(r-1)

Adjust Variables

First term (a)
a =
150
Common ratio (r)
r =
0.22.5

Sum of first n terms of a GP. For |r| < 1, the sum approaches a/(1-r) as n→∞.

Real-World Applications

Total investment returns — FD with compound interest over multiple years.

Mortgage total — Sum of all EMI payments with interest.

Bouncing ball — Total distance: initial height + 2×sum of bounce heights.

Zeno's paradox — Achilles catches the tortoise: infinite GP sum.

Annuity valuation — Present value of future payments.

Network effect — Total users when each brings r new users.

Fractal lengths — Koch snowflake perimeter: infinite geometric series.

Signal processing — Decaying echo sums.

Pension fund — Total corpus from geometric contributions.

Carbon absorption — Trees absorbing decreasing amounts yearly.

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