How do you DO THIS?
4+8+12+16+20... +392+ 396+ 400?
To solve this problem, we need to find the sum of an arithmetic series. An arithmetic series is a series of numbers in which the difference between consecutive terms is constant.
In this case, the common difference between consecutive terms is 4 (every term is increased by 4). The first term in the series is 4, and we need to find the sum up to the term 400. To find the number of terms in this series, we can subtract the first term from the last term and divide the result by the common difference:
Number of terms = (Last Term - First Term) / Common Difference
Number of terms = (400 - 4) / 4 = 396 / 4 = 99
So, we have an arithmetic series with 99 terms.
To find the sum of an arithmetic series, we can use the formula:
Sum = (n/2)(first term + last term)
where "n" is the number of terms in the series.
Applying this formula to our problem, we have:
Sum = (99/2)(4 + 400)
Sum = (99/2)(404)
Sum = 99(202)
Sum = 19998
Therefore, the sum of the series 4 + 8 + 12 + 16 + 20 + ... + 392 + 396 + 400 is 19,998.