Question

fill in the missing numbers to complete the pattern:
□, 3.47, □, 3.57, 3.62, 3.67

Explanation:

Step1: Find the common difference

Look at the last three numbers: \(3.57\), \(3.62\), \(3.67\). The difference between \(3.62 - 3.57 = 0.05\) and \(3.67 - 3.62 = 0.05\). Wait, but between \(3.47\) and \(3.57\), the difference is \(3.57 - 3.47 = 0.10\), which is two steps. So the common difference per step is \(0.05\)? Wait, no, let's check again. Wait, \(3.62 - 3.57 = 0.05\), \(3.67 - 3.62 = 0.05\). Then between \(3.47\) and the next missing number, then to \(3.57\). Let's see the positions:

Let the sequence be \(a_1\), \(a_2 = 3.47\), \(a_3\), \(a_4 = 3.57\), \(a_5 = 3.62\), \(a_6 = 3.67\)

Check the difference between \(a_5\) and \(a_6\): \(3.67 - 3.62 = 0.05\)

Between \(a_4\) and \(a_5\): \(3.62 - 3.57 = 0.05\)

Ah, so the common difference \(d = 0.05\)

Now, \(a_4 = a_3 + 0.05\), so \(a_3 = a_4 - 0.05 = 3.57 - 0.05 = 3.52\)

Then, \(a_2 = a_1 + 0.05\), so \(a_1 = a_2 - 0.05 = 3.47 - 0.05 = 3.42\)

Step2: Verify the sequence

Now the sequence is \(3.42\), \(3.47\), \(3.52\), \(3.57\), \(3.62\), \(3.67\). Let's check the differences:

\(3.47 - 3.42 = 0.05\)

\(3.52 - 3.47 = 0.05\)

\(3.57 - 3.52 = 0.05\)

\(3.62 - 3.57 = 0.05\)

\(3.67 - 3.62 = 0.05\)

All differences are \(0.05\), so the pattern holds.

Answer:

The missing numbers are \(3.42\) and \(3.52\) (in order, the first blank is \(3.42\), the second blank is \(3.52\))