I have the following recursive formula the for a sequence:
{V1=1Vn=Vn−1+nn>1
This sequence increases by n for each term increase. Now I need to find if 3003 is a value of this sequence. I managed to solve the problem by finding an explicit formula for the sequence and solved in terms of n. Like this:
3003=(n−1)n2+n
which led to
n=77∨n=−78
So since there's no negative terms in a sequence I concluded that when n=77, 3003 is the value of the sequence.
What I would like to know is if there is some other simpler/direct way to solve this.
I realized that the value of the nth term is the sum of all terms below n, including it (n,n−1,n−2,…,0) and came up with that explicit formula but it isn't obvious.
