very basic linear non-homogeneous recurrence relation where difference increases by 1 each recursion

Question

I'm trying to find a formula for this sequence. 2, 4, 7, 11, 16, ...

Please let me know what I'm doing wrong.

$a_{n} – a_{n-1} = n$

Homogeneous case $a_{n} – a_{n-1} = 0$:
Characteristic equation $r – 1 = 0$ gives $1^n$ is a solution

Non-homogeneous case $a_n – a_{n-1} = n$:
Let $b_n = cn + d$ be a solution

Then $cn + d – c(n-1) - d = n$

So $(c - c - 1)n + (d – d) = 0$