Answer
The recursive definition for this sequence is
$a_{n} = a_{n-1} + n +1$ where $a_{1} = 0$
Work Step by Step
Look for simple addition or multiplication patterns between consecutive terms.
Here, the differences increase by $1$ every term:
$a_{2} - a_{1} = 3-0 = 3$
$a_{3} - a_{2} = 7-3 = 4$
$a_{4} - a_{3} = 12-7= 5$
$a_{5} - a_{4} = 18-12= 6$
Hence, the pattern is
$a_{n} = a_{n-1} + n +1$ and the first term is $a_{1} = 0$.
