Math: Sum of Geometric Series?

Question

An author published a book which was being sold online. The first month the author sold 14400 books, but the sales were declining steadily at 5% each month. If this trend continues, how many total books would the author have sold over the first 23 months, to the nearest whole number?

Steve4Physics · Accepted Answer

This is a simple geometric series with
a₁ = 14400
r = 0.95 (multiplying by 0.95 is the same as reducing by 5%

Sₙ  = a₁(1 - rⁿ)/(1-r)

For 23 months
S₂₃ = 14400(1 - 0.95²³)/(1-0.95) = 199481

Math: Sum of Geometric Series?

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