Question

fill in the missing numbers to complete the pattern:
5.97, □, □, 6.03, 6.05, 6.07
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Explanation:

Step1: Identify the pattern

Looking at the given numbers 6.03, 6.05, 6.07, we can see that the difference between consecutive terms is \(6.05 - 6.03= 0.02\) and \(6.07 - 6.05 = 0.02\). So the common difference \(d = 0.02\).

Step2: Find the first missing number

To find the first missing number (let's call it \(a_2\)) after 5.97 (\(a_1 = 5.97\)), we use the formula for an arithmetic sequence \(a_{n}=a_{n - 1}+d\). So \(a_2=a_1 + d=5.97+ 0.02 = 5.99\).

Step3: Find the second missing number

To find the second missing number (let's call it \(a_3\)), we use the same formula. \(a_3=a_2 + d=5.99+ 0.02=6.01\). We can check that \(6.01+0.02 = 6.03\) which matches the given sequence.

Answer:

The missing numbers are \(5.99\) and \(6.01\) (in order). So the completed pattern is \(5.97, 5.99, 6.01, 6.03, 6.05, 6.07\)