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Concept · Functions & Sequences
Geometric sequences
general term a1·qn-1, sum, geometric mean, partial-sum form Sn=a·bn+c constraints, monotonicity conditions
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Key formulas
7- Arithmetic nth terman = a1 + (n − 1)d
- Arithmetic sumSn = n(a1 + an)/2 = n·a1 + n(n−1)d/2 (quadratic in n)
- Geometric nth terman = a1·rn−1
- Geometric sum (r ≠ 1): Sn = a1(1 − rn)/(1 − r)
- Geometric mean of a,bG = ±√ab
- Term from partial suman = Sn − Sn−1 for n ≥ 2, a1 = S1
- Geometric-series partial-sum form Sn = A·rn + C requires A + C = 0
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