waheguru 3 years ago I don't understand this question The sum of the first "n" natural numbers is a quadratic relation. Determine that relation and verify it for the first 6 natural numbers

1. Mertsj

We would be talking about the sum of this arithmetic series: 1,2,3,4,5,...n-1, n

2. waheguru

Can you show me step by step how to solve this

3. Mertsj

I don't really know. I would hunt up the formula for the sum of an arithmetic series and see where that leads me.

4. Mertsj
5. electrokid

natural number sequence is 1, 2, 3, 4, 5,/// notice that "0" is not a natural number

6. electrokid

this is an arithmatic sequence of difference "1" so, $S_n={n\over2}[a_0+(n-1)d]\\ S_n={n\over2}[1+(n-1)]\\ S_n={n^2\over2}$

7. waheguru

can you explain how you came up with the formula

8. electrokid

the formula $S_n={n\over2}[a_0+(n-1)d]$ is the formula for the sum of "n" numbers in arithmetic series starting from "a0" with a common difference of "d"