Answer: 13,467
Step-by-step explanation:
The first multiply of 3 after 100 is 102 (102/3 = 34) and the last multiple of three before 301 is 300 (300/3 = 100).
So, we can organize the multiples of 3 in a sequence: (102, 105, ..., 297, 300).
As we can see, we have an arithmetic sequence above, with the following parameters:
first term = a1 = 102
last term = an = 300
number of terms = n = ?
common difference = d = 3
First, we have to find the number of terms of this sequence. To do this, we can use the following formula:
[tex]\begin{gathered} an=a_1+(n-1)\cdot d \\ 300=102+(n-1)\cdot3 \\ 300-102=(n-1)\cdot3 \\ 198=(n-1)\cdot3 \\ \frac{198}{3}=n-1 \\ 66=n-1 \\ 66+1=n \\ n=67 \end{gathered}[/tex]Now, we can use the formula for the sum (S) of the arithmetic sequence and find the sum of the terms:
[tex]\begin{gathered} S=\frac{n\cdot(a_1+an)}{2} \\ S=\frac{67\cdot(102+300)}{2} \\ S=13,467 \end{gathered}[/tex]The sum is 13,467.
