TITLE: Seat location in a concert hall where number of seats increases with each row
QUESTION [2 upvotes]: Problem
Your friend buys you a concert ticket for seat 995 in a concert hall with 65 seats in row one, 67 seats in row 2, and 69 seats in row three, and so on. The seats are numbered from left to right, so the first seat in row one is 1 and the first seat in row two is 66 and so on. The concert hall has 40 rows of seats.

A. How many seats are in the last row?

I found this answer to be 143 using arithmetic sequence formulas.

B. How many seats are in the concert hall?

I found this to be 4160 using Sum of Sequence formula $S_n$.

C. Describe the location of your seat.

This one I'm stuck on, any ideas?

REPLY [1 votes]: Row $n$ has $63+2n$ seats.  
The first seat in row $n$ is $1+\sum_{k=1}^{n-1} (63 + 2k)$, which is: $n^2+62 n-62$ 
You are in seat $995$.   By inspection that's in which row and what seat?

IE: Find row $n$ such that:
$$n^2+62n - 62 \quad \leq\quad 995 \quad < \quad (n+1)^2+62(n+1)-62$$
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