Question

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

Answer 1

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....

Answer 2

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.