In the sequence 100, 50, 25, 12.5, and 6.25, what is the common ratio in decimal form?

In the sequence 100, 50, 25, 12.5, and 6.25, what is the common ratio in decimal form?

• A. 0.25
• B. 0.5
• C. 2.0
• D. 1.5

Answer: (B)

To determine the common ratio in the given sequence, we can look at the relationship between consecutive terms. A common ratio in a geometric sequence is found by dividing a term by its preceding term. Starting with the first two terms of this sequence, we have: - The first term is 100. - The second term is 50. Calculating the ratio, we divide the second term by the first term: 50 ÷ 100 = 0.5. Next, if we check the ratio between the second and third terms: - The second term is 50. - The third term is 25. Calculating this ratio gives: 25 ÷ 50 = 0.5. We can confirm this consistency by examining the next pair: - The third term is 25. - The fourth term is 12.5. So: 12.5 ÷ 25 = 0.5. Finally, we can check the last pair: - The fourth term is 12.5. - The fifth term is 6.25. Calculating this results in: 6.25 ÷ 12.5 = 0.5. Since all pairs of terms maintain the same ratio when divided, we find that the

To determine the common ratio in the given sequence, we can look at the relationship between consecutive terms. A common ratio in a geometric sequence is found by dividing a term by its preceding term.

Starting with the first two terms of this sequence, we have:

• The first term is 100.

• The second term is 50.

Calculating the ratio, we divide the second term by the first term:

50 ÷ 100 = 0.5.

Next, if we check the ratio between the second and third terms:

• The second term is 50.

• The third term is 25.

Calculating this ratio gives:

25 ÷ 50 = 0.5.

We can confirm this consistency by examining the next pair:

• The third term is 25.

• The fourth term is 12.5.

So:

12.5 ÷ 25 = 0.5.

Finally, we can check the last pair:

• The fourth term is 12.5.

• The fifth term is 6.25.

Calculating this results in:

6.25 ÷ 12.5 = 0.5.

Since all pairs of terms maintain the same ratio when divided, we find that the