Answer:
To find the explicit formula for this sequence, we need to determine the common ratio between successive terms. To do this, we can divide any term by the previous term. For example:
6 ÷ 2 = 3
18 ÷ 6 = 3
54 ÷ 18 = 3
162 ÷ 54 = 3
So the common ratio is 3.
Next, we can use the general form of a geometric sequence to find the explicit formula:
a(n) = a(1) * r^(n-1)
where a(n) is the nth term of the sequence, a(1) is the first term, r is the common ratio, and n is the position of the term we want to find.
In this sequence, a(1) = 2 and r = 3. So the explicit formula for this sequence is:
a(n) = 2 * 3^(n-1)
For example, if we want to find the 6th term, we can plug in n = 6:
a(6) = 2 * 3^(6-1) = 2 * 3^5 = 2 * 243 = 486
Therefore, the 6th term of the sequence is 486.