What could be the next term in the geometric sequence 2, 6, 18, 54?

What could be the next term in the geometric sequence 2, 6, 18, 54?

• A. 108
• B. 162
• C. 144
• D. 128

Answer: (A)

In a geometric sequence, each term is found by multiplying the previous term by a fixed non-zero number called the common ratio. To identify the common ratio in this sequence, we can examine the relationship between consecutive terms. Starting with the first two terms: - From 2 to 6, we multiply by 3 (2 × 3 = 6). - From 6 to 18, we again multiply by 3 (6 × 3 = 18). - From 18 to 54, we continue the pattern and multiply by 3 (18 × 3 = 54). We can confirm the common ratio is consistently 3. Therefore, to find the next term in the sequence following 54, we multiply it by the common ratio of 3. Calculating this: 54 × 3 = 162. Thus, the next term in the geometric sequence is 162, making it the correct answer.

In a geometric sequence, each term is found by multiplying the previous term by a fixed non-zero number called the common ratio. To identify the common ratio in this sequence, we can examine the relationship between consecutive terms.

Starting with the first two terms:

• From 2 to 6, we multiply by 3 (2 × 3 = 6).

• From 6 to 18, we again multiply by 3 (6 × 3 = 18).

• From 18 to 54, we continue the pattern and multiply by 3 (18 × 3 = 54).

We can confirm the common ratio is consistently 3. Therefore, to find the next term in the sequence following 54, we multiply it by the common ratio of 3.

Calculating this:

54 × 3 = 162.

Thus, the next term in the geometric sequence is 162, making it the correct answer.