2. Inductive and Deductive Reasoning
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What do the differences between the consecutive terms have in common?
Pattern: see solution
Next two numbers: 30, 42
We will begin by finding the pattern. Then, we will be able to find the next two numbers.
This means that we have to take a different approach. Let's take a closer look at the differences between the consecutive terms. 2, 4, 6, 8 All of the numbers above are even and positive. What is more, we can tell that they are consecutive even numbers. Therefore, the pattern is adding consecutive even numbers to the previous terms.
Let's use the pattern to find the next two numbers. First, we have to determine the even number that we need add to the last known term, 20. This will be 10, since it is the first even number that comes after 8. 20+ 10=30 The next even number is 12. Now, we can find the number that comes after 30. 30+12=42