Answer:
Option B. an = 3• 6ⁿ¯¹
Explanation:
The following data were obtained from the question:
First generation = 3
2nd generation = 1st generation x 6
2nd generation = 3 x 6 = 18
3rd generation = 2nd generation x 6
3rd generation = 18 x 6 = 108
Therefore, we can thus form a sequence as:
3, 18, 108
Since the 2nd term is obtained by multiplying the previous term (i.e the 1st term) by 6 and also, the 3rd is obtained by multiplying the 2nd by 6, the sequence is a geometric progression.
Thus,
The common ratio (r) = 6
The first term (a) = 3
The nth term (an) =?
The nth term of geometric progression is given as
an = arⁿ¯¹
Inputing the value of the first term (a) and common ratio (r) into the above equation, we obtained:
an = arⁿ¯¹
an = 3• 6ⁿ¯¹
Therefore, the explicit formula which can be used to find the number of rabbits in the nth generation is
an = 3• 6ⁿ¯¹