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12 cards from this deck
Mathematical relationship connecting each sequence value to the previous value
an+1=p⋅an+qa_{n+1} = p \cdot a_n + qan+1=p⋅an+q
Multiplier: growth (p>1p>1p>1), shrink (0<p<10<p<10<p<1), constant (p=1p=1p=1)
Constant: fixed amount added at each step
Initial condition (starting value of sequence)
q=0q = 0q=0 (no constant being added each step)
an=a0⋅pna_n = a_0 \cdot p^nan=a0⋅pn
an=(a0−q1−p)⋅pn+q1−pa_n = (a_0 - \frac{q}{1-p}) \cdot p^n + \frac{q}{1-p}an=(a0−1−pq)⋅pn+1−pq
q1−p\frac{q}{1-p}1−pq
Long-term value sequence approaches when ∣p∣<1|p| < 1∣p∣<1
an=a0+nqa_n = a_0 + nqan=a0+nq
Linear growth (simply add qqq at each step)
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