Answer:
The number of seat when n is odd 
The number of seat when n is even 
Step-by-step explanation:
Given that, each successive row contains two fewer seats than the preceding row.
Formula:
The sum n terms of an A.P series is
![S_n=\frac{n}{2}[2a+(n-1)d]](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D)
![=\frac{n}{2}[a+l]](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bn%7D%7B2%7D%5Ba%2Bl%5D)
a = first term of the series.
d= common difference.
n= number of term
l= last term
term of a A.P series is

n is odd:
n,n-2,n-4,........,5,3,1
Or we can write 1,3,5,.....,n-4,n-2,n
Here a= 1 and d = second term- first term = 3-1=2
Let
of the series is n.

Here
, n=t, a=1 and d=2

⇒(t-1)2=n-1




Last term l= n,, the number of term
, First term = 1
Total number of seat
![S_n=\frac{\frac{n+1}{2}}{2}[1+n}]](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7B%5Cfrac%7Bn%2B1%7D%7B2%7D%7D%7B2%7D%5B1%2Bn%7D%5D)
![=\frac{{n+1}}{4}[1+n}]](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%7Bn%2B1%7D%7D%7B4%7D%5B1%2Bn%7D%5D)


n is even:
n,n-2,n-4,.......,4,2
Or we can write
2,4,.......,n-4,n-2,n
Here a= 2 and d = second term- first term = 4-2=2
Let
of the series is n.

Here
, n=t, a=2 and d=2

⇒(t-1)2=n-2




Last term l= n, the number of term
, First term = 2
Total number of seat
![S_n=\frac{\frac{n}{2}}{2}[2+n}]](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7B%5Cfrac%7Bn%7D%7B2%7D%7D%7B2%7D%5B2%2Bn%7D%5D)
![=\frac{{n}}{4}[2+n}]](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%7Bn%7D%7D%7B4%7D%5B2%2Bn%7D%5D)
