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