Answer:
1078
Step-by-step explanation:
Total no of rows (n) = 22
Since, 18, 20, 22 ..... forms an arithmetic sequence with first term (a) = 18 and common difference (d) = 2.
We need to find: Total no of seats in the theatre [tex](S_{22}).[/tex]
Formula to be used:
[tex]S_{n}= \frac{n}{2}\bigg[2a+(n-1)d\bigg][/tex]
Plug the values of a, d and n in the above formula, we find:
[tex]\implies S_{22}= \frac{22}{2}\bigg[2(28)+(22-1)(2)\bigg][/tex]
[tex]\implies S_{22}=11[56+(21)(2)][/tex]
[tex]\implies S_{22}=11[56+42][/tex]
[tex]\implies S_{22}=11[98][/tex]
[tex]\implies S_{22}=1078[/tex]
Thus, there are total 1078 seats in the theatre.
