Answer:
There are 54 seats in 14th row,
In the first 14th row the total seats are 483.
Step-by-step explanation:
Given,
The number of seats in first row = 15,
Also, 3 additional seats in each subsequent row,
⇒ The seats in second row = 15 + 3 = 18,
⇒ The seats in third row = 18 + 3 = 21,
⇒ The seats in fourth row = 21 + 3 = 24,
................................................, so on,........
Thus, the given situation can be written as an AP,
15, 18, 21, 24,...........
Having first term, a = 15,
Common difference, d = 3,
Thus, the number of seats in 14th row,
[tex]a_{14}=a+(14-1)3=15+13(3)=15+39=54[/tex]
Also, the total number of seats in total in the first 14th seats,
[tex]S_{14}=\frac{14}{2}[2a+(14-1)d]=7(2\times 15+13(3))=7(30+39)=7(69)=483[/tex]
