prove that the sum of the integers is

**The positive integers are bracketed as follows:**

(1), (2,3), (4,5,6), . . .

where there are r integers in the rth bracket. Prove that the sum of the integers in the rth bracket is

$\displaystyle \frac{r}{2} (r^2 +1)$

this is what I did

using the formula for arithmetic sequence,

we know that there are r integers. and the difference is 1

so that becomes

Sum of r integers = $\displaystyle \frac{r}{2}(2a + (r-1)) $ where a is the first term of the sequence

However, I can't figure out what a (a.k.a the first term) is equal to

any ideas?

thanks