Question

Write the explicit rule for the following sequence: 2, 6, 18, 54, 162

A. an = 22^(n-1)
B. an = 63^(n-1)
C. an = 32^(n-1)
D. an = 23^(n-1)

Answer 1

The explicit rule for the given sequence is an = 3^(n-1).

Step-by-step explanation:

The explicit rule for the given sequence is an = 3^(n-1).

To find the explicit rule, we notice that each term is obtained by multiplying the previous term by 3. This means that the common ratio between consecutive terms is 3. Using this information, we can write the expression for the nth term as an = a1 * r^(n-1), where a1 is the first term (2) and r is the common ratio (3). Substituting these values, we get an = 2 * 3^(n-1).