To find the salary for the next three years, we are going to use the formula for the nth term of a geometric sequence:
where
is the nth term of the sequence
is the first term in the sequence
is the common ratio
is the position of the term in the sequence
To check if the values $400 and 400(1.05) for a geometric sequence, we are going to find their common ratio. To find the common ratio, we are going to use the formula
where
is the current term in the sequence
is the previous term in the sequence
We can infer from our values, that the current term of the sequence is 400(1.5), so
. That leaves 400 as the previous term, so
. Lets replace those values in our formula to find
:
Now that we have our common ratio, we can replace it in our formula for the nth term to find the athlete's salary for each of the next three years. Notice that the first term of our sequence is $400, so
We can conclude that the athlete's salary for each of the next three years is: $441,$463.05,486.2025 respectively. Also, those vales for a geometric sequence because they share a common ratio, (1.05).
