Question 38570
<pre><font size = 5><b>How many 3 digit counting numbers are even?

This is the arithmetic sequence

100, 102, 104, ··· , 998

a<sub>n</sub> = a<sub>1</sub> + (n-1)d

To find d:

d = 102 - 100 = 104 - 102 = 2

a<sub>1</sub> = 100

a<sub>n</sub> = 998

a<sub>n</sub> = a<sub>1</sub> + (n-1)d

998 = 100 + (n-1)(2)

998 = 100 + 2(n-1)

998 = 100 + 2n - 2

998 = 98 + 2n

900 = 2n

450 = n

So there are 450 three-digit counting numbers

Edwin
AnlytcPhil@aol.com</pre>