Question

An author published a book which was being sold online. The first month the author sold 27500 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 6 months, to the nearest whole number?

Answer 1

The total number of books sold in the first six months is approximately 128,951, calculated using the formula for the sum of a geometric series with initial sales of 27,500 books and a monthly decline of 10%.

Step-by-step explanation:

To calculate the total number of books an author would have sold over the first six months, with sales declining by 10% each month, we'll use the formula for the sum of a geometric series. The initial number of books sold in the first month is 27500. The common ratio of the geometric series, which represents the monthly decline in sales, is 0.9 (since the sales decline by 10%, 100% - 10% = 90% or 0.9 in decimal form).

The sum of the first six terms of a geometric series is given by:

Sn = a1 × (1 - rn)/(1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms.

Using the formula, we have:

S6 = 27500 × (1 - 0.96)/(1 - 0.9)

Calculating the sum:

S6 = 27500 × (1 - 0.531441)/(1 - 0.9)

S6 = 27500 × (0.468559)/0.1

S6 ≈ 27500 × 4.68559

S6 ≈ 128951

Therefore, the author would have sold approximately 128951 books over the first six months, to the nearest whole number.