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

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.