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Geometric Sequence

★★☆☆☆Middle School

📖Definition

A sequence where the ratio between consecutive terms is constant.

aₙ = a₁ · r^n-1

General term formula

Sₙ = (a₁(1 - rⁿ))/(1 - r) = (a₁(rⁿ - 1))/(r - 1) (r ≠ 1)

Sum of geometric sequence

S_∈fty = (a₁)/(1 - r) (|r| < 1)

Sum of infinite geometric series

예제 1★★☆☆☆

Find the 5th term of geometric sequence with a₁ = 2, r = 3.

예제 2★★★☆☆

Find the sum: 1 + 1/2 + 1/4 + 1/8 + ...

Compound interest

Exponential growth

Binary tree node count

#algebra#sequence#geometric