What is the next term in the geometric sequence: 3, 9, 27?

What is the next term in the geometric sequence: 3, 9, 27?

• A. 54
• B. 81
• C. 90
• D. 63

Answer: (B)

In a geometric sequence, each term is found by multiplying the previous term by a constant called the common ratio. To identify the next term in the sequence provided (3, 9, 27), first, we need to determine the common ratio. To find the common ratio, divide the second term by the first term: 9 ÷ 3 = 3. Now take the third term and divide it by the second term: 27 ÷ 9 = 3. From this, we can confirm that the common ratio is consistent and equal to 3. To find the next term, we multiply the last known term (27) by the common ratio (3): 27 × 3 = 81. Thus, the next term in the sequence is 81. This means the answer is correctly identified, as the calculations demonstrate the progression of the geometric sequence based on the established common ratio.

In a geometric sequence, each term is found by multiplying the previous term by a constant called the common ratio. To identify the next term in the sequence provided (3, 9, 27), first, we need to determine the common ratio.

To find the common ratio, divide the second term by the first term:

9 ÷ 3 = 3.

Now take the third term and divide it by the second term:

27 ÷ 9 = 3.

From this, we can confirm that the common ratio is consistent and equal to 3. To find the next term, we multiply the last known term (27) by the common ratio (3):

27 × 3 = 81.

Thus, the next term in the sequence is 81. This means the answer is correctly identified, as the calculations demonstrate the progression of the geometric sequence based on the established common ratio.