What do you calculate to find the common ratio of a geometric sequence?

What do you calculate to find the common ratio of a geometric sequence?

• A. Sum of terms
• B. Difference between consecutive terms
• C. Ratios of consecutive terms
• D. Products of terms

Answer: (C)

To find the common ratio of a geometric sequence, you calculate the ratios of consecutive terms. In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor, known as the common ratio. This means that if you take any two consecutive terms in the sequence, dividing the second term by the first term will give you the common ratio. For example, consider the geometric sequence 2, 6, 18. To find the common ratio, you would divide the second term (6) by the first term (2), resulting in a ratio of 3. Similarly, dividing the third term (18) by the second term (6) also gives a ratio of 3. This consistency across the terms confirms that the common ratio is indeed 3, showing how ratios of consecutive terms directly yield the common ratio in a geometric progression.

To find the common ratio of a geometric sequence, you calculate the ratios of consecutive terms. In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor, known as the common ratio. This means that if you take any two consecutive terms in the sequence, dividing the second term by the first term will give you the common ratio.

For example, consider the geometric sequence 2, 6, 18. To find the common ratio, you would divide the second term (6) by the first term (2), resulting in a ratio of 3. Similarly, dividing the third term (18) by the second term (6) also gives a ratio of 3. This consistency across the terms confirms that the common ratio is indeed 3, showing how ratios of consecutive terms directly yield the common ratio in a geometric progression.