If the sequence 2, 6, 18, 54, 162 continues, what is the next number?

To determine the next number in the sequence 2, 6, 18, 54, 162, we need to identify the pattern or rule that is applied to generate the sequence.

Let's observe the relationship between consecutive terms:

• From 2 to 6, the multiplication factor is 3 (2 × 3 = 6).

• From 6 to 18, the multiplication factor is also 3 (6 × 3 = 18).

• From 18 to 54, again, the multiplication factor is 3 (18 × 3 = 54).

• From 54 to 162, the multiplication factor remains 3 (54 × 3 = 162).

It is evident that each term is obtained by multiplying the previous term by 3. To find the next number after 162, we continue this pattern:

162 × 3 = 486.

This shows that the next number in the sequence is 486, confirming that the correct answer is indeed C.