In the sequence $x_0, x_1, x_2, ..., x_n$, each term from $x_1$ to $x_k$ is 3 greater than the previous term, and each term from $x_{k+1}$ to $x_n$ is 3 less than the previous term, where $n$ and $k$ are positive integers and $k<n$. If $x_0=x_n=0$ and $x_k=15$, what is the value of $n$?

Thanks for the clear explanation! I initially missed that the sequence increases by 3 up to x_k then decreases by 3. That symmetry makes it click.

Why is the answer 10 and not 15? I get that x_k=15, but I'm confused about how n relates to k.

Medium difficulty for me. The tricky part was realizing that k is the index where the sequence changes direction, not the number of terms. Once I set x_0=0 and x_k=15 with +3 steps, it was straightforward.

Is there a faster way to solve this without writing out the sequence? I got the right answer but it took me longer than 2 minutes.