Question

What is the explicit rule for the nth term of the geometric sequence 4, 12, 36, 108, 324, ...?

1) an = 4(3n)
2) an = 3(4n – 1)
3) an = 4(3n – 1)
4) an = 4(3n + 1)

Answer 1

an = 4(3n – 1)

Step-by-step explanation:

took test

Answer 2

The explicit rule for the nth term of the given geometric sequence is an = 4(3n – 1), which is option 3 in the list provided.

Step-by-step explanation:

The explicit rule for the nth term of the geometric sequence 4, 12, 36, 108, 324, ... is seeking a formula that allows us to find any term of the sequence without listing all the terms. This sequence has a common ratio, which is the factor we multiply by to go from one term to the next. In this case, each term is three times the previous term, so our common ratio (r) is 3.

To find the nth term of a geometric sequence, we use the formula an = a1 * r^(n-1), where an is the nth term, a1 is the first term, and r is the common ratio. For this sequence, the first term (a1) is 4.

Substituting the known values into our formula gives us: an = 4 * 3^(n-1). Therefore, the correct explicit rule for the nth term is option 3) an = 4(3n – 1).