In a music stadium, 35th row has 120 seats
and explicit formula is [tex]a_{n}=3n+15[/tex] is explicit formula for given sequence.
Step-by-step explanation:
In music stadium, there are 18 seats in first row and 21 seats in second row and it is continuously increasing by 3
Here, Arithmetic sequence is 18,21,24,27.....120
There Arithmetic sequence is given as a,a+d,a+d......a+(n-1)d
Where, a = First term = 18 and d = Increment = 3
Q (a) Write an explicit rule to model the sequence formed by the number of seats in each row.
Now, Create an explicit formula
[tex]a_{n}=a+(n-1)d[/tex]
[tex]a_{n}=18+(n-1)(3)[/tex]
[tex]a_{n}=18+(3n-3)[/tex]
[tex]a_{n}=3n+15[/tex] is explicit formula for given sequence.
Q (b) Use the rule to determine which row has 120 seats.
Given [tex]a_{n}=120[/tex]
To determine which row has 120 seats.
[tex]a_{n}=3n+15[/tex]
[tex]120=3n+15[/tex]
[tex]105=3n[/tex]
[tex]n=35[/tex]
Therefore, 35th row has 120 seats
