Question

The students in a college marching band are arranged in rows. The recursive rule f(n) = f(n − 1) + 8 and f(1) = 13 gives the number of students in each row, where n is the row number. All of the clarinet players are in row 1, and all of the trumpet players are in row 4. How many more trumpet players than clarinet players are there? Complete the explanation.

Answer 1

There are 24 more trumpet players than clarinet players

Explanation:

The given information are;

The recursive rule or the number of band members in a row is f(n) = f(n - 1) + 8

Where f(1) = 13

The members of the band players in row 1 = The clarinet players

The members of the band players in row 4 = The trumpet players

Therefore, the number of clarinet players = f(1) = 13

The number of band members in row 2, f(2) = f(1) + 8 = 13 + 8 = 21

The number of band members in row 3, f(3) = f(2) + 8 = 21 + 8 = 29

The number of band members in row 4, f(4) = f(3) + 8 = 29 + 8 = 37

Therefore, given that the trumpet players are in row 4, the number of trumpet players = The number of band members in row 4 = 37 Trumpet players

The difference in the number of trumpet and clarinet = The number of more trumpet players than clarinet players = 37 - 13 = 24 more trumpet players than clarinet players

There are 24 more trumpet players than clarinet players.