must be answered with a series/sequences formula
over the past 10 years, the number of CD's sold by a mail order music company has increased an average of 12% per year. If the company sold 1.5 million CD's ten years ago, the total number of sales they have made over all ten years is...?
The accumulation of sales over the 10 year period derives from the geometric progression with first term of a = 1,5500,000, the the yearly increase of 12%, or common factor of r = 1.12 and the period of interest, namely n = 10 years.
The sum of the 10 yearly sales is then S = a(r^n - 1)/(r-1) or
S = 1,500,000(1.12^10 - 1)/(1.12 - 1).
I'll let you punch out the numbers.
To find the total number of CD sales over the past 10 years, we can use the formula for the sum of a geometric series:
Sn = a * (r^n - 1) / (r - 1)
where:
Sn = sum of the series
a = first term of the series
r = common ratio (percent increase + 100%, converted to decimal)
n = number of terms
In this case, we know that the first term (a) is 1.5 million CDs, the percent increase is 12% per year (or 0.12 as a decimal), and there are 10 years (n) in total.
Let's plug in these values into the formula:
Sn = 1.5 million * (1 + 0.12)^10 - 1 / 0.12 - 1
Simplifying the equation:
Sn = 1.5 million * (1.12)^10 - 1 / 0.12 - 1
Calculating the value:
Sn ≈ 1.5 million * (3.138428376) - 1 / 0.12 - 1
≈ 1.5 million * 41.417710000
≈ 62,126,565
Therefore, the mail order music company has made approximately 62,126,565 CD sales over the past 10 years.