1.1 Sum of a Arithmetic sequence / progression

Sum of a Arithmetic sequence / progression

Let sequence = {1,2,3,4,5,...n}

Then what is {1+2+3+4+5+...+n} ?

Solution:

What matters is the first and last,
Add them and cut them half,
Number of the numbers in a multiply,
You get the sum in a single try!

First number = 1
Last number = n
Add them and cut them half = (1+n)/2
Number of numbers = n   Since (1 to n are n numbers)
In a multiply = n* (1+n)/2

So sum = n*(1+n)
                  -----------
                       2
Generic formula:
Let sequence ={a1,a2,a3...an}
Sum  =    n*(a1+an)
                  -----------
                       2