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Sequences & Series
AP Precalculus · Unit 2
Learning Objectives
Arithmetic vs Geometric sequences
Explicit formulas: aₙ = a₁ + (n−1)d
Partial sums Sₙ visualization
Convergence of infinite geometric series
Formulas
Arithmetic:
aₙ = a₁ + (n−1)d
Sₙ = n(a₁ + aₙ)/2
Geometric:
aₙ = a₁ · r^(n−1)
Sₙ = a₁(1 − rⁿ)/(1 − r)
S∞ = a₁/(1 − r), |r| < 1
Tags
arithmetic
geometric
series
convergence
Sequence Terms aₙ
Partial Sums Sₙ
SEQUENCE TYPE
Arithmetic: aₙ = a₁ + (n−1)d
Geometric: aₙ = a₁ · r^(n−1)
Geometric |r|<1 (Convergent)
Harmonic: aₙ = 1/n
First Term a₁
2.0
Common Diff d
3.0
Common Ratio r
2.0
Terms N
15
aₙ (last term)
—
Sₙ (partial sum)
—
S∞ (infinite sum if convergent)
—
Top chart: individual terms aₙ
Bottom chart: cumulative partial sums Sₙ