Question

In the 1st generation, there are 6 squirrels in a forest. Every generation after that, the squirrel population multiplies by 4. In generation 2 there are 24 squirrels, in generation 3 there are 96 squirrels, and so on. Which explicit formula can be used to find the number of squirrels in the nth generation?

Answer 1

The appropriate choice is

... B. an = 6·4^(n-1)

The general term of a geometric sequence with first term a1 and common ratio r is given by

... an = a1·r^(n-1)

Your sequence has a1=6 and r=4. The answer above is the result of substituting the given numbers for the corresponding variables in the general formula.

Answer 2

Answer:

Option B is correct.i.e., No of squirrels in nth generation $a_n=6\times4^{n-1}$

Step-by-step explanation:

Given:

No of squirrels in 1st Generation = 6

No of squirrels in 2nd generation = 24

No of squirrels in 3rd generation = 96

Option A).

No of squirrels in nth generation $a_n=4\times6^{n-1}$

From formula,

No of squirrels in 1st generation $a_1=4\times6^{1-1}=4$

So, This option is wrong.

Option B).

No of squirrels in nth generation $a_n=6\times4^{n-1}$

From formula,

No of squirrels in 1st generation $a_1=6\times4^{1-1}=6$

No of squirrels in 2nd generation $a_2=6\times4^{2-1}=6\times4=24$

No of squirrels in 3rd generation $a_3=6\times4^{3-1}=6\times16=96$

So, This option is correct.

Therefore, Option B is correct.i.e., No of squirrels in nth generation $a_n=6\times4^{n-1}$