Question

fill in the missing numbers to complete the pattern;
5.66, , 5.86, 5.96, , 6.16

Explanation:

Step1: Find the common difference

Looking at the given numbers \(5.66\), \(5.86\), \(5.96\), \(6.16\), we calculate the difference between consecutive terms. For example, \(5.86 - 5.66 = 0.2\)? Wait, no, \(5.96 - 5.86 = 0.1\), and \(6.16 - 5.96 = 0.2\)? Wait, no, let's check again. \(5.86 - 5.66 = 0.2\)? Wait, no, \(5.96 - 5.86 = 0.1\), so maybe the common difference is \(0.1\). Let's verify: \(5.66 + 0.1 = 5.76\), then \(5.76 + 0.1 = 5.86\) (which matches), \(5.86 + 0.1 = 5.96\) (matches), \(5.96 + 0.1 = 6.06\), and \(6.06 + 0.1 = 6.16\) (matches). So the common difference is \(0.1\).

Step2: Find the first missing number

The first missing number is after \(5.66\), so we add \(0.1\) to \(5.66\): \(5.66 + 0.1 = 5.76\).

Step3: Find the second missing number

The second missing number is after \(5.96\), so we add \(0.1\) to \(5.96\): \(5.96 + 0.1 = 6.06\).

Answer:

The missing numbers are \(5.76\) and \(6.06\). So the sequence is \(5.66, \boldsymbol{5.76}, 5.86, 5.96, \boldsymbol{6.06}, 6.16\).