Question

The arithmetic sequence 2, 4, 6, 8, 10,. . . Represents the set of even natural numbers. What is the 100th even natural number? a100 = What is the sum of the first 100 even natural numbers? S100 = Complete the sentence below with less than, greater than, or equal to. The sum of the first 100 even natural numbers is the sum of the first 101 odd natural numbers.

Answer 1

The 100th even natural number is 200

Given the sequence 2, 4, 6, 8, 10....

The nth term of the sequence is expressed as:

Tn  = a + (n - 1)d

a is the first term = 2

d is the common difference = 4 - 2 = 6 - 4 = 2

n is the number of terms

Substitute the given parameters into the formula

Tn = 2(n-1)2

Tn = 2+(2n - 2)

Tn = 2n

Get the 100th term

T10=  2(100) = 200

Hence the 100th even natural number is 200

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Answer 2

Answer:

1)

200

2)  

10100

3)

less than

Step-by-step explanation:

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