Answer:
Option B. 60300
Step-by-step explanation:
The given expression [tex]\sum_{n=1}^{200}(3n)[/tex] represents an arithmetic sequence. [3, 6, 9, 12,..............]
In this sequence first term a = 3
common difference d = 3
and number of terms n = 200
We have to find the sum of first 200 terms of this sequence.
Formula of the sum of an arithmetic sequence is [tex]=\frac{n}{2}[2a+(n-1)d][/tex]
Now we put the values in the formula
[tex]\sum_{n=1}^{200}(3n)=\frac{200}{2}[2(3)+(200-1)(3)][/tex]
= [tex]100[6+(199)(3)]=100[6+597][/tex]
= [tex]100(603)[/tex]
= 60300
Therefore option B. 60300 is the answer.
