Mathematics Sequence

Question

The population of a particular city begins at 2,500 and doubles every year. What is the population in the city after 9 years?

Answer 1

This looks like a geometric sequence. The formula for this would be

a_n=a₁(r)^n-1

a₁ is the initial value = 2500

r is the common ratio = 2 because it is doubling every year

n the number of years = 9

Plugging these into the equation

a₉=2500(2)^(9-1) = 640,000 is the population of the city after 9 years

I used a table to check my work as well. (Not good if you were doing too many years but 9 isn't bad)

Answer 2

At the end of year 1 the sequence is 5000

At the end of year 2 the sequence is10,000 etc

In general at the end of year n the sequence is 2500 x 2ⁿ

So at the end of year 9 the sequence is 2500 x 2⁹ = 1,280,000