The given sequence is a geometric sequence with a common ratio of 3. The 10th term of the sequence is 3,888.
The given sequence is: 6, 18, 54, 162, and 486.
These numbers follow a geometric sequence. In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio.
In this case, the common ratio can be found by dividing any term by its previous term. Let's use the second and first terms: 18 ÷ 6 = 3.
Therefore, the common ratio is 3. To find the 10th term, we can use the formula for a geometric sequence: an = a1 * r^(n-1), where an represents the nth term, a1 represents the first term, r represents the common ratio, and n represents the position of the term we want to find.
For this sequence, a1 = 6, r = 3, and n = 10.
Plugging the values into the formula, we get: a10 = 6 * 3^(10-1) = 6 * 3^9 = 3,888.
Therefore, the 10th term of the sequence is 3,888.