summing series

The formula for the sum of 1 from 1 to n = n
The formula for the sum of r from 1 to n = (n(n+1))
The question asks to derive the arithmetic series using these formula.
I have tried putting a into formula 1 and (n-1)d into formula 2 and adding them but I don,t seem to get anywhere. Could anyone tell me if I am on the right track or point me in the right direction please. Thank you.

You got the right approach, though hopefully you subbed in (r-1)d and not (n-1)d into the second formula.

In fact the priblem is the same as evaluating

sum of (a-d) + sum of (rd)

where both sums run from r=1 to n.

Also youre missing a factor of 1/2 for your second formula.

The formula I end up with is:
an + ((r-1)d)((r-1)d +1))/2. I cannot see how this compares to the arithmetic series.

You are not understanding...

Sum of arithmetic series with first term $a$ and common difference $d$ is given by

$\displaystyle \sum_{r=1}^n a+(r-1)d$

which can be recast into the form

$\displaystyle (a-d)\sum_{r=1}^n 1 + d \sum_{r=1}^n r$

and now you apply the formulae.

Thank you for your help. I get it now. I am finding this topic a bit difficult.