Question

The leopard population in an African wildlife area is currently 17. Due to a new conservation effort, conservationists hope the leopard population will increase by 4 animals each year for the next 20 years. Which explicit rule represents the leopard population sequence?

Answer 1

`a{_n} = 17 + (n - 1)4` for n = 1, 2, . . . , 20.

Explanation:

This is an arithmetic sequence, because the population is said to increase by 4 animals yearly. The formula for the nth term in an arithmetic sequence is given by:

`a{_n} = a{_1} + (n - 1)d` where
`a_n` is the nth term, [/tex]a_1[/tex] is the first term, n = 1, 2, . . . and d is the common difference.

Since they are currently 17, this implies that the first number in the population sequence will be 17. In order words, the first term is 17.

Since they increase by 4 yearly, then the common difference is 4.

Since it's for 20years, the n = 1, 2, . . ., 20. The explicit formula is therefore:

`a{_n} = 17 + (n - 1)4` for n = 1, 2, . . . , 20.