Question

the first year a toy manufacturer introduces a new toy, it sales total $495,000. the company expects it sales to drop 10% each succeeding year. find the total expected sales in the first 6 years

Answer 1

Sales acting like this would produce a geometric sequence with a common ratio of 90/100 or 0.9 because each term would be 0.9 time the previous term.

The sum of a geometric sequence is:

s(n)=a(1-r^n)/(1-r), a=initial term, r=common ratio, n=term number, in this case:

s(n)=495000(1-0.9^n)/(1-0.9)

s(n)=495000(1-0.9^n)/(0.1)

s(n)=4950000(1-0.9^n) so

s(6)=4950000(1-0.9^6)

s(6)=$2630632.95