SOLUTION: Find the sum of the following numbers. 1 2 3 4 ... 50 2 3 4 5 ... 51 3 4 5 6 ... 52 . . . . ... . . . . . ... . . . . . ... . 50 51 52 53 ... 99

Algebra ->  Sequences-and-series -> SOLUTION: Find the sum of the following numbers. 1 2 3 4 ... 50 2 3 4 5 ... 51 3 4 5 6 ... 52 . . . . ... . . . . . ... . . . . . ... . 50 51 52 53 ... 99      Log On


   



Question 1209377: Find the sum of the following numbers.
1 2 3 4 ... 50
2 3 4 5 ... 51
3 4 5 6 ... 52
. . . . ... .
. . . . ... .
. . . . ... .
50 51 52 53 ... 99

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

The sum of the first n positive integers is %28n%28n%2B1%29%29%2F2.

So the first term is the sum of the first 50 positive integers is 

50%2851%29%2F2=1275

Then to get the second term, we add 1 to each one of those 50, which adds 50.
We add 50 each time to get the next term.

So it's an arithmetic series with 1st term 1275 and common difference 50,
with 50 terms.

S%5Bn%5D=+expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%29

S%5B50%5D=+expr%2850%2F2%29%28+2%2A1275%2B%2850-1%29%2A50+%29

That works out to be 125000.

Edwin