An auditorium has 20 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. how many seats are in the auditorium?

there are 580 seats

Step-by-step explanation:

The number of seats in each row is increasing in arithmetic progression.

The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[(2a + (n - 1)d]

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 10 seats

d = 2 seats (the seats in each row are increasing by 2)

n = 20(number of rows)

We want to determine the number of seats in 20 rows. Therefore

S20 = 20/2[(2×10 + (20 - 1)2]

S20 = 10(20 + 38) = 10×58

S = 580

anser is a

step-by-step explanation:

negitive slope

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x