Given:
The number of seats in the first row is <em>a</em>₁ = 12.
The series of the increasing number of seats is 12, 14, 16......
The objective is to find the total number of seats in the first 12 rows.
Explanation:
The difference between the number of seats in each row can be calculated by the difference between the successive terms of the series.
![\begin{gathered} d=14-12=2 \\ d=16-14=2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20d%3D14-12%3D2%20%5C%5C%20d%3D16-14%3D2%20%5Cend%7Bgathered%7D)
The number of rows to be calculated is <em>n</em> = 12.
To find the number of seats:
The number of seats presents in the first 12 rows can be calculated as,
![S_n=\frac{n}{2}\lbrack2a_1+(n-1)d\rbrack](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Bn%7D%7B2%7D%5Clbrack2a_1%2B%28n-1%29d%5Crbrack)
On plugging the obtained values in the above equation,
![\begin{gathered} S_{12}=\frac{12}{2}\lbrack2(12)+(12-1)2\rbrack \\ =6\lbrack24+11(2)\rbrack \\ =6(46) \\ =276 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20S_%7B12%7D%3D%5Cfrac%7B12%7D%7B2%7D%5Clbrack2%2812%29%2B%2812-1%292%5Crbrack%20%5C%5C%20%3D6%5Clbrack24%2B11%282%29%5Crbrack%20%5C%5C%20%3D6%2846%29%20%5C%5C%20%3D276%20%5Cend%7Bgathered%7D)
Hence, the total number of seats in the first 12 rows is 276.
Answer:
1087.5
Step-by-step explanation:
870/12=72.5
72.5*15=1087.5