Question

An author published a book which was being sold online. The first month the author sold 21000 books, but the sales were declining steadily at 12% each month. If this trend continues, how many total books would the author have sold over the first 9 months, to the nearest whole number?

Answer 1

Answer: 119,616

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Step-by-step explanation:

The author sells 21,000 books in the first month.

Then they sell 21,000*(1-0.12) = 21,000*(0.88) = 18,480 in the second month.

Then they sell 18,480*(1-0.12) = 18,480*(0.88) = 16,262.4 = 16,262 in the third month.

And so on. These values follow a geometric sequence with first term a = 21,000 and common ratio r = 0.88

We can think of the 0.88 as 88% of the original value (since losing 12%, we keep the remaining 88%)

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Use the formula below to sum the first 9 terms of the geometric sequence

Plug in a = 21000 and r = 0.88

`S_n = a*(1-r^n)/(1-r)\\\\S_9 = 21000*(1-0.88^9)/(1-0.88)\\\\S_9 \approx 21000*(0.6835216)/(0.12)\\\\S_9 \approx 21000*5.6960133\\\\S_9 \approx 119,616.2793\\\\S_9 \approx 119,616\\\\`

The author sold about 119,616 books over the course of the first nine months.