An author published a book which was being sold online. The first month the author sold 22100 books, but the sales were declining steadily at 10% each month. If this trend continues, how many total books would the author have sold over the first 22 months, to the nearest whole number? Answer:

Question

An author published a book which was being sold online. The first month the author sold 22100 books, but the sales were declining steadily at  10% each month. If this trend continues, how many total books would the author have sold over the first 22 months, to the nearest whole number? Answer:

Bytelearn · Accepted Answer

Identify initial number and decrease: Identify the initial number of books sold and the monthly percentage decrease. The author sold 22100 books in the first month and sales are declining by 10% each month.Recognize geometric sequence: Recognize that the situation describes a geometric sequence where each term is 90% (or 0.9 times) of the previous term, because of the 10% decrease. The first term (a1) is 22100, and the common ratio (r) is 0.9.Use formula for sum: Use the formula for the sum of the first n terms of a geometric sequence to find the total number of books sold over the first 22 months. The formula is S_n = a1 * (1 - r^n) / (1 - r), where S_n is the sum of the first n terms, a1 is the first term, r is the common ratio, and n is the number of terms.Calculate sum of first 22 terms: Calculate the sum of the first 22 terms using the formula. S_22 = 22100 * (1 - 0.9^22) / (1 - 0.9)Perform calculations: Perform the calculations. S_22 = 22100 * (1 - 0.9^22) / 0.1 First, calculate 0.9^22. 0.9^22 ≈ 0.095617924991195Calculate 0.9^22: Continue the calculation by subtracting this value from 1. 1 - 0.095617924991195 ≈ 0.904382075008805Subtract from 1: Divide this result by 0.1 to find the multiplier for the initial number of books sold. 0.904382075008805 / 0.1 ≈ 9.04382075008805Divide by 0.1: Multiply this value by the initial number of books sold to find the total number of books sold over the first 22 months. 22100 * 9.04382075008805 ≈ 199969.45Multiply by initial number: Round the result to the nearest whole number, as the question asks for the total number of books to the nearest whole number. 199969.45 rounds to 199969.

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