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The arithmetic sequence 2, 4, 6, 8, 10, . . . represents the set of even natural numbers. What is the 100th even natural number? a100 =

User Corliss
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You can use this rule to find any even natural number. Multiply the position of the number by 2 to find the number. In this example, you would take 100 times 2 to get 200. I used the given pattern to figure this out. 2 x 2 = 4, 2 x 3 = 6, 2 x 4 = 8, 2 x 5 = 10, etc....
User Heinzi
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Answer: The 100th even natural number is 200.

Step-by-step explanation: Given that the following arithmetic sequence represents the set of natural numbers :

2, 4, 6, 8, 10, . . ..

We are given to find the 100th even natural number, i.e., the 100-th term of the sequence.

We know that

the n-th term of an arithmetic sequence with first term a and common difference d is given by


a_n=a+(n-1)d.

For the given sequence, we have

a = 2 and d = 4 - 2 = 6 - 4 = . . . =2.

Therefore, the 100-th term of the sequence will be


a_(100)=a+(100-1)d=2+99*2=2+198=200.

Thus, the 100th even natural number is 200.

User Mateusz Chrzaszcz
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