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10 cards from this deck
A sequence with a constant difference between terms.
an=a1+(n−1)da_n = a_1 + (n-1)dan=a1+(n−1)d
Sn=n/2(2a1+(n−1)d)S_n = n/2(2a_1 + (n-1)d)Sn=n/2(2a1+(n−1)d) or Sn=n/2(a1+an)S_n = n/2(a_1 + a_n)Sn=n/2(a1+an)
Each term is found by multiplying the previous term.
an=a1rn−1a_n = a_1 r^{n-1}an=a1rn−1
Sn=a1(1−rn)/(1−r)S_n = a_1(1 - r^n)/(1 - r)Sn=a1(1−rn)/(1−r) for r≠1r ≠ 1r=1
S∞=a11−rS_\infty = \frac{a_1}{1 - r}S∞=1−ra1
Use a geometric sequence for exponential growth.
Total savings Tn=n2(2a1+(n−1)d)T_n = \frac{n}{2}(2a_1 + (n-1)d)Tn=2n(2a1+(n−1)d)
Rn=P(1+r)n−M⋅(1+r)n−1rR_n = P(1+r)^n - M \cdot \frac{(1+r)^n - 1}{r}Rn=P(1+r)n−M⋅r(1+r)n−1
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