Learning Resources

Focus C: Population Growth

First of all, review the definition of a geometric sequence given in the side note on page 14 of your text. From Focus C, we can generalize that in a geometric sequence the first term is listed and subsequent terms are found by multiplying a previous term by a constant. Consider the sequence {3, 6, 12, 24, ...}. This satisfies the definition of a geometric sequence. The common ratio is 2. A recursive formula for the sequence would be: 

= 3, = 2 if n >1, n ? N. 

This means that each new term is found by multiplying the previous term by 2. An explicit formula describing the same sequence would be

= 3 x 2^{n - 1} where n ? N  

The 10^th term of the sequence would be found by finding the value of 3 x 2⁹.