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Geometric Sequence
Middle School
Definition
A sequence where the ratio between consecutive terms is constant.
Formulas
aₙ = a₁ · r^n-1
General term formula
- aₙnth term
- a₁First term
- rCommon ratio
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
Examples
Example 1
Find the 5th term of geometric sequence with a₁ = 2, r = 3.
Example 2
Find the sum: 1 + 1/2 + 1/4 + 1/8 + ...
Applications
Finance
Compound interest
Demographics
Exponential growth
Computing
Binary tree node count
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