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Mkey [24]
2 years ago
11

An author published a book which was being sold online. The first month the author sold 21000 books, but the sales were declinin

g 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?
Mathematics
1 answer:
Wittaler [7]2 years ago
4 0

Answer:  119,616

You may have to erase the comma when inputting the answer.

=======================================================

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%)

-------------

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*\frac{1-r^n}{1-r}\\\\S_9 = 21000*\frac{1-0.88^9}{1-0.88}\\\\S_9 \approx 21000*\frac{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.

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