Question

fill in the missing numbers to complete the pattern:
□, 5.2, 5.4, □, 5.8, 6.0

Explanation:

Step1: Identify the pattern

Looking at the given numbers \(5.2\), \(5.4\), \(5.8\), \(6.0\), we can see that the difference between consecutive terms is \(5.4 - 5.2=0.2\), \(6.0 - 5.8 = 0.2\). So the common difference \(d = 0.2\).

Step2: Find the first missing number

To find the first missing number (let's call it \(a_1\)), we know that the next term \(a_2=5.2\). Using the arithmetic sequence formula \(a_{n}=a_{n - 1}+d\), for \(n = 2\), we have \(a_2=a_1 + d\). So \(a_1=a_2 - d\). Substituting \(a_2 = 5.2\) and \(d=0.2\), we get \(a_1=5.2-0.2 = 5.0\).

Step3: Find the second missing number

To find the second missing number (let's call it \(a_4\)), we know that \(a_3 = 5.4\) and \(d = 0.2\). Using the arithmetic sequence formula \(a_{n}=a_{n - 1}+d\), for \(n=4\), we have \(a_4=a_3 + d\). Substituting \(a_3=5.4\) and \(d = 0.2\), we get \(a_4=5.4 + 0.2=5.6\).

Answer:

The first missing number is \(5.0\) and the second missing number is \(5.6\)