Answer: First Option
The number of multiples of 9 is 211
Step-by-step explanation:
Note that the first multiplo of 9 between 100 and 2000 is number 108. The last multiple of 9 is 1998.
If we use the arithmetic sequence to perform the calculation
[tex]a_n = a_1 + d(n - 1)[/tex]
So the first term [tex]a_1[/tex] is:
[tex]a_1 = 108[/tex]
The last term [tex]a_n[/tex] is
[tex]a_n = 1998[/tex]
The common difference is
[tex]d = 9[/tex]
Thus
[tex]1998 = 108 + 9(n-1)[/tex]
We solve the equation for n and obtain the number of multiples of 9.
[tex]1998-108 = 9(n-1)\\\\\frac{1998-108}{9}=n-1\\\\n = 210 +1\\\\n = 211[/tex]
