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?

A. 803
B. 60,300
C. 120,600
D. 360,000

Answer 1

Option B. 60300

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
`=(n)/(2)[2a+(n-1)d]`

Now we put the values in the formula

`\sum_(n=1)^(200)(3n)=(200)/(2)[2(3)+(200-1)(3)]`

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

=
`100(603)`

= 60300

Therefore option B. 60300 is the answer.