In the 1st generation, there are 3 rabbits in a meadow. every generation after that, the rabbit population multiplies by 6. in generation 2 there are 18 rabbits, in generation 3 there are 108 rabbits, and so on. which explicit formula can be used to find the number of rabbits in the nth generation?

Step-by-step explanation:

This is a geometric sequence, since each term is found by multiplying the previous term by a constant (called the common ratio).

The explicit formula for a geometric sequence is

, where a₁ is the first term and r is the common ratio.

In this sequence, the first term is 3 and the common ratio is 6; this gives us

Using the product property of exponents, we can write the power of 6 as

Something raised to the -1 power is "flipped"; since 6 = 6/1, this means we have 1/6:

Using the commutative property, we multiply the 3 and the 1/6:

Simplifying, we have

there is no question content here, but you for the free points! : d