Round #647

What is the next term in the sequence 2, 6, 18, 54?

The given sequence is 2, 6, 18, 54. To find the pattern, let's examine how each term relates to the previous one: - From 2 to 6: \(2 \times 3 = 6\) - From 6 to 18: \(6 \times 3 = 18\) - From 18 to 54: \(18 \times 3 = 54\) We can see that each term is obtained by multiplying the previous term by 3. This indicates that the sequence follows a geometric progression with a common ratio of 3. To find the next term in the sequence, we multiply the last given term (54) by the common ratio (3): \[54 \times 3 = 162\] Therefore, the next term in the sequence is **162**.

The next term in the sequence 2, 6, 18, 54 can be determined by observing the pattern of multiplication. Each term is obtained by multiplying the previous term by 3. Let's break it down: - \(2 \times 3 = 6\) - \(6 \times 3 = 18\) - \(18 \times 3 = 54\) Following this pattern, the next term would be: \[54 \times 3 = 162\] So, the next term in the sequence is **162**.