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Operations on Rational and Irrational Numbers
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John's payments are
month 1: $100
month 2: $100*(1.1)
month 3: $100*(1.1)²
month 4: $100*(1.1)³
...
The payments form the geometric sequence
a, ar, ar², ..., arⁿ
where
a = $100
r = 1.1
The sum of the first n terms is
Therefore the sum of the first 20 payments is
S₂₀ = [$100(1 - 1.1²⁰)]/(1 - 1.1)
= $5727.50
John makes a total of $5727.50 in the first 20 payments.
month 1: $100
month 2: $100*(1.1)
month 3: $100*(1.1)²
month 4: $100*(1.1)³
...
The payments form the geometric sequence
a, ar, ar², ..., arⁿ
where
a = $100
r = 1.1
The sum of the first n terms is
Therefore the sum of the first 20 payments is
S₂₀ = [$100(1 - 1.1²⁰)]/(1 - 1.1)
= $5727.50
John makes a total of $5727.50 in the first 20 payments.