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Since the numbers are getting larger, the rule is likely to add a number. Find the difference between the first two numbers. Test if adding this number works on the rest of the pattern.What is the rule for this pattern? 2, 6, 10, 14, 18

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Answer:

 

Step-by-step explanation:

Applying the given rule on the given set, we get

The difference between first two numbers is=6-2=4, the difference between next two numbers=10-6=4, the difference between next two numbers=14-10=4 and the difference between next two numbers=18-14=4.

We can see that there is a constant result in the difference of every number of the given data, thus it is satisfying the Arithmetic progression with first number a=2 and the common difference d=4, then

[tex]T_{n}=a+(n-1)d[/tex]

=2+(n-1)4

=2+4n-4

=4n-2

Thus, the rule for the given pattern will be: 4n-2.

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