What is the Geometric Progression for Rabbit Population Growth?

[thereddevils]

Homework Statement

Number of rabbits reared by Alice at the beginning of certain year is given as b. End of that particular year, the number of rabbits were given as 10+(3/2) b . Write down the number of rabbits at the end of second and third year. Find the total number of rabbits at the end of nth year.

Homework Equations

The Attempt at a Solution

It doesn't tell whether the increase in the number of rabbits is an AP or GP but it could have been a GP according to the next part of the question. Assuming that its a GP,

common ratio, r= (20+3b)/(2b)

Then, T2 = (10+3/2 b)((20+3b)/(2b))

??

 

[D H]

It doesn't tell whether the increase in the number of rabbits is an AP or GP but it could have been a GP according to the next part of the question.

While a geometric progression certainly makes more sense than an arithmetic progression here, what makes you think those are the only two options? All you have been told here is the relation between the population at the start and end of year 1. So, generalize this. Assume that the population at the end of some year is 10 + 3/2 times the population at the start of that year. Note that the population at the start of some year is the same as the population at the end of the previous year.

 

[cyby]

Just to further this point - it really is neither - if you write down a few terms, you will clearly see that it is neither arithmetic or geometric, so what you know about these two types of series goes out the window.

 

[thereddevils]

ok thanks. I got T2=25+(3/2)^2 b and T3=95/2+(3/2)^3 b. How do i find the total population at the nth year?

 

[cyby]

Why don't you start by writing the the sums for the first, second, and third years, and maybe see a pattern?