Respuesta :
The number of rows in the considered theater which has 3 more seats that seats that the previous row, with first row having 15 and last row having 78 seats is given by: Option D: 22
What is arithmetic sequence?
An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
[tex]a, a + d, a + 2d, ... , a + (n+1)d, ...[/tex]
Its nth term is
[tex]T_n = a + (n-1)d[/tex]
(for all positive integer values of n)
And thus, the common difference is
[tex]T_{n+1} - T_n[/tex]
for all positive integer values of n
For this case, we can use arithmetic sequence as the number of seats in each next row is 3 more than previous row, so there is constant difference.
Now, the first number is 15, so we have: a = 15,d = 3 (increasing, so positive).
Let there are 'n' row in the theater.
Then the nth term of the arithmetic sequence having a = 15 and d = 3 should be 78 (as the nth row from first to last is the last row, having 78 seats).
Thus, we get:
[tex]T_n = a + (n-1)d\\78 = 15 + (n-1)3\\78-15 =3n - 3\\\\n = \dfrac{63+3}{3} = 22[/tex]
Thus, the number of rows in the considered theater which has 3 more seats that seats that the previous row, with first row having 15 and last row having 78 seats is given by: Option D: 22
Learn more about arithmetic sequence here:
https://brainly.com/question/3702506
