An amphitheatre has 20 seats in the first​ row, 24 in the​ second, 28 in the​ third, and so​ on, for 29 rows. How many seats are in the​ amphitheatre?

Question

An amphitheatre has 20 seats in the first​ row, 24 in the​ second, 28 in the​ third, and so​ on, for 29 rows. How many seats are in the​ amphitheatre?

Answer 1

row 1 has 20 seats

row 2 has 24 seats

row 3 has 28 seats

row n has 20+4(n-1)

row 29 has 20+4(28) = 20+ 112 = 132 seats

sum of the arithmetic sequence,with n=29, a1 =20, a29 = 132

is S29 = (n/2)(a1 +a29)

= 29/2)(20+132)

= 29/2)(152)

= 29(76)

= 2204 total seats

sum of an arithmetic sequence = half the number of terms times (the first term plus the last term)