Given:
The number of seats in the first row is a₁ = 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.
[tex]\begin{gathered} d=14-12=2 \\ d=16-14=2 \end{gathered}[/tex]The number of rows to be calculated is n = 12.
To find the number of seats:
The number of seats presents in the first 12 rows can be calculated as,
[tex]S_n=\frac{n}{2}\lbrack2a_1+(n-1)d\rbrack[/tex]On plugging the obtained values in the above equation,
[tex]\begin{gathered} S_{12}=\frac{12}{2}\lbrack2(12)+(12-1)2\rbrack \\ =6\lbrack24+11(2)\rbrack \\ =6(46) \\ =276 \end{gathered}[/tex]Hence, the total number of seats in the first 12 rows is 276.
