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10 cards from this deck
It has a common ratio between terms.
un=ar(n−1)u_n = ar^{(n-1)}un=ar(n−1)
Divide a term by its previous term.
Sn=a(1−rn)/(1−r)S_n = a(1 - r^n) / (1 - r)Sn=a(1−rn)/(1−r)
Subtract rSnrS_nrSn from SnS_nSn and simplify.
un=3⋅(−4)(n−1)u_n = 3 \cdot (-4)^{(n-1)}un=3⋅(−4)(n−1)
aaa is the first term of the sequence.
Solve ar(n−1)<10,000ar^{(n-1)} < 10,000ar(n−1)<10,000 using logarithms.
r=32/0.5=64r = 32 / 0.5 = 64r=32/0.5=64; ratio doubles each term.
a=0.5/4=0.125a = 0.5 / 4 = 0.125a=0.5/4=0.125
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