Question

A geometric sequence can be used to describe the population of rabbits on a farm. The first spring the farmer purchased 10 rabbits. Four years later there are 810 rabbits at the farm. Assuming that none of the rabbits leave the​ farm, how many rabbits were on the farm in year 4​?

Answer 1

First term in geometric progression is a= 10.

After 4 years a₅= 810

The n^th term is t_n=a*r^n-1.

So 10*r^5-1=810,

r⁴=81,

r⁴=3⁴.

Thus, r= 4.

Required is t₄=10*3^4-1

= 10*3³

=10*27

=270.

So there were 270 rabbits on the farm in the year 4.