Answer:
80,200
Explanation:
There is a formula for the sum of a series of numbers from a_1 to a_n.
S = (a_n * a_n+1)/2
This formula means: multiply the last number of the series by what would be the next number, and divide by 2.
The last number you have is 400. The next number would be 401.
Multiply 400 by 401 and divide by 2. That is the sum of the 400 numbers.
S = (401 * 402)/2
S = 160400/2
S = 80200
Answer: The sum is 80,200
Here's a way to understand the formula.
You are adding 400 numbers, from 1 to 400.
Write the first 200 numbers on a line:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ... 198 199 200
Now write the next 200 numbers, from 201 to 400 under these numbers, but start from 400 and go down 1 each number to the right.
You end up with these two lines:
1 2 3 4 5 6 7 8 9 ... 198 199 200
400 399 398 397 396 395 394 393 392 ... 203 202 201
Now add every two numbers in the same column.
1 2 3 4 5 6 7 8 9 ... 198 199 200
400 399 398 397 396 395 394 393 392 ... 203 202 201
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401 401 401 401 401 401 401 401 401 ... 401 401 401
Now you have 200 times the number 401.
200 * 401 = 80,200