First 3-digit number divisible by 12 is 108.
Last 3-digit number divisible by 12 is 996.
108 = 12 · 9
996 = 12 · 83
From 108 to 996 are 83 - 9 + 1 = 75 numbers divisible by 12.
108 is the first term of the arithmetic sequence.
996 is the 75th term of the arithmetic sequence.
Use the formula of a sum of terms of an arithmetic sequence:
[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n[/tex]
We have:
[tex]a_1=108,\ a_{75}=996,\ n=75[/tex]
Substitute:
[tex]S_{75}=\dfrac{108+996}{2}\cdot75=(552)(75)=41,400[/tex]
