Question

Scarlett bought an ant farm with 80 ants. From the following week forward, the ant population tripled every week. Let a(n) be the number of the ants in Scarlett’s farm in the nth week since she got it.
Is this arithmetic or geometric sequence!
a(n)=
How Mann ants after 8 weeks?

Answer 1

Answer:

$a(n) = 80(3)^{n}$

524880

Step-by-step explanation:

Scarlett bought an ant farm with 80 ants. From the following week forward, the ant population tripled every week.

So, the population of ant after 1st week will be (80 × 3) = 240

Again, after 2 weeks this will be (240 × 3) = 720

Therefore, the ant population is increasing in a geometric sequence and here the first term is 80 and the common ratio is 3.

Hence, if a(n) is the population of ant after n weeks then,  

$a(n) = 80(3)^{n}$  (Answer)

Now, there will be $80(3)^{8} = 524880$ ants after 8 weeks. (Answer)

Answer 2

Answer: It is a geometric sequence

g(n) = 80•3^n-1

Step-by-step explanation:

The first term is the initial and population size, which is 80 ants. The common ratio is the factor by which the ant population increases each week, which is 3.