Question

Zhang lei tracked the size of the bear population in a nature reserve. The first year, there were 1000 bears. Sadly, the population lost 10% of its size each year. Let f(n) be the number of bears in the reserve in the nth year since Zhang lei started tracking it. f is a sequence. What kind? f(1)= f(n)= f(n-1) */+ ____

Answer 1

A geometric sequence

Explanation:

A geometric sequence is a sequence one in which each next term is found by multiplying the previous term by a constant.

In our case, we are facing a 10% population loss every year, which means to find the bear population next year when have to multiply the population of the previous year by 0.9; thus, we a multiplying the previous term by a constant to get the next term: this is a geometric sequence.

The first term
`f(1)` of this geometric series is the bear population in the first year, which is 1000; thus,

`f(1)=1000`

and for the nth term
`f(n)`:

`f(n)=f(n-1)*0.9`.