Respuesta :
The total number of 3 digit even numbers is 450
Step-by-step explanation:
Step 1 :
We need to determine the number of 3 digit numbers which is even and the leftmost digit is not zero .
The 3 digits with left most digit not equal to zero starts from 100 and goes up to 998
If we consider only the even 3 digit numbers in this interval, this would form an arithmetic progression with the first number a = 100 and the common difference d = 2.
Step 2:
The last number l in this series is 998 .
So we have
a = 100
l = 998
d = 2
The nth term in the arithmetic progression is given by a + (n-1) d
so substituting the above values we get
100 + (n-1) 2 = 998
2n = 900 => n = 450
Step 3 :
Answer :
The total number of 3 digit even numbers is 450
There are 450 three-digit even numbers where the leftmost digit cannot be zero
The smallest even three-digit is 100, and the largest even three-digit is 998.
The difference between consecutive even numbers is 2.
So, the count of even numbers is calculated using the following arithmetic progression formula
[tex]\mathbf{L = a + (n - 1)d}[/tex]
Where:
[tex]\mathbf{L = 998}[/tex] -- the last term
[tex]\mathbf{a = 100}[/tex] -- the first term
[tex]\mathbf{d = 2}[/tex] -- the common difference
So, we have:
[tex]\mathbf{L = a + (n - 1)d}[/tex]
[tex]\mathbf{998 = 100 + (n -1) \times 2}[/tex]
Subtract 100 from both sides
[tex]\mathbf{898 = (n -1) \times 2}[/tex]
Divide both sides by 2
[tex]\mathbf{449 =n -1}[/tex]
Add 1 to both sides
[tex]\mathbf{n = 450}[/tex]
Hence, there are 450 three-digit even numbers
Read more about arithmetic progressions at:
https://brainly.com/question/13989292
