Question

The expression (picture) represents the sum of the first 200 multiples of 3. What is the sum of the first 200 multiples of 3?

Answer 1

Answer:

Option B. 60300

Step-by-step explanation:

The given expression $\sum_{n=1}^{200}(3n)$ 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 $=\frac{n}{2}[2a+(n-1)d]$

Now we put the values in the formula

$\sum_{n=1}^{200}(3n)=\frac{200}{2}[2(3)+(200-1)(3)]$

= $100[6+(199)(3)]=100[6+597]$

= $100(603)$

= 60300

Therefore option B. 60300 is the answer.