Question

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

a) an=4×3n
b) an=3×(4n−1)
c) an=4×(3n−1)
d) an=4×(3n+1)

Answer 1

The explicit rule for the nth term of the geometric sequence 4, 12, 36, 108, 324 is an = 4 × 3^(n-1).

Step-by-step explanation:

The explicit rule for the nth term of a geometric sequence can be found by observing the pattern in the given sequence. In this case, we can see that each term is obtained by multiplying the previous term by 3. Therefore, the explicit rule for this geometric sequence is an = 4 × 3^(n-1).