Rina Will Hold Her Piano Recital At The Music Hall The Music Hall Has 12 Rows Of Seats In Which The First Row Has 15 Seats Each Succeding Row Has 3 Mo

rina will hold her piano recital at the music hall the music hall has 12 rows of seats in which the first row has 15 seats each succeding row has 3 more seats that the one in front of it

 

Answer:

There are 48 seats in the 12th or last row.

There are 378 total seats in the music hall.

Step-by-step explanation:

Total rows, n = 12

First row, a₁ = 15

Common difference in increasing number of seats from first row, d = 3

Find the number of seats in the last row, a₁₂:

an = a₁ + (n-1)(d)

a₁₂ = 15 + (12-1)(3)

a₁₂ = 15 + (11)(3)

a₁₂ = 15 + 33

a₁₂ = 48

There are 48 seats in the last row, the 12th row.

Find the total number of seats in the music hall:

Sn = n/2 (a₁ + an)

S₁₂ = 12/2 (15 + 48)

S₁₂ = 6(63)

S₁₂ = 378

There are 378 total seats in the music hall.