Question

A geometric sequence can be used to describe the population of rabbits on a farm. The first spring the farmer purchased 4 rabbits. Four years later there are 64rabbits at the farm Assuming that none of the rabbits leave the farm, how many rabbits were on the farm in year 3?rabbits (Type a whole number)

Answer 1

Answer:

There were 25 rabbits on the farm in year 3

Step-by-step explanation:

The sequence described is as follows:

4, x, y 64

This shows that the first term, a is 4, and the common ratio, r is x/4 or y/x or 64/y

The nth term of the geometric series is given as:

`T_n=ar^(n-1)`

To obtain the third term, we put n = 3

`\begin{gathered} T_3=4*((64)/(y))^(3-1) \\ \\ y=4*((64)/(y))^2 \\ \\ y^3=4*64^2 \\ \\ y^3=16384 \\ \\ y=(16384)^{(1)/(3)}\approx25 \end{gathered}`

There were 25 rabbits on the farm in year 3