Question

what is the next term of the geometric sequence?
2, 6, 18, \boxed{}

Explanation:

Step1: Find the common ratio

In a geometric sequence, the common ratio \( r \) is found by dividing a term by its previous term. So, \( r=\frac{6}{2} = 3\) (or \( r=\frac{18}{6}=3\)).

Step2: Calculate the next term

The next term (the 4th term) is found by multiplying the last given term (18) by the common ratio \( r \). So, the next term \( = 18\times3=54\).

Answer:

54