SOLUTION: An audio-visual room (AVR) at Adamson University has 7 seats on the first row, 10 on the second row, 13 on the third row, and so on, and 40 rows of seats. How many seats are in the

Question 1197143: An audio-visual room (AVR) at Adamson University has 7 seats on the first row, 10 on the second row, 13 on the third row, and so on, and 40 rows of seats. How many seats are in the AVR?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Please see this similar question before reading onward
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1197145.html
This similar question may help you solve the problem on your own.
If you still need help, then the solution is in the next section below.

-----------------------

We have an arithmetic sequence since the gap between terms is the same.
10-7 = 3
13-10 = 3
Each time we get to a new row, we add on 3 seats.
This is the common difference.
d = common difference = 3

The first term is a1 = 7

Summary so far
a1 = 7
d = 3

Let's form the nth term of the arithmetic sequence
an = a1 + d(n-1)
an = 7 + 3(n-1)

As a check, let's plug in n = 2 and we should get 10 seats
an = 7 + 3(n-1)
a2 = 7 + 3(2-1)
a2 = 10
That works out. I'll let you verify other values of n.

Now plug in n = 40
an = 7 + 3(n-1)
a40 = 7 + 3(40-1)
a40 = 124
There are 124 seats in row 40.

Now apply this summation formula
Sn = sum of the first n terms of an arithmetic sequence
Sn = (n/2)*(firstTerm + nthTerm)
S40 = (40/2)*(firstTerm + 40thTerm)
S40 = 20*(7 + 124)
S40 = 2620

An alternative formula is this
Sn = (n/2)*(2*a1 + d(n-1))
S40 = (40/2)*(2*7 + 3*(40-1))
S40 = 2620

The verification process is similar to that shown in the link above.

-----------------------

Answer: 2620 seats total

RELATED QUESTIONS
an auditorium has 50 rows of seats. There are 8 seats in the first row, 10 seats in the... (answered by josmiceli)

An auditorium has 20 seats on the first row, 24 seats on the second row, 28 seats on the... (answered by richwmiller)

An auditorium has 20 seats on the first row, 24 seats on the second row, 28 seats on the... (answered by addingup,ikleyn,MathTherapy)

A classroom has stadium seating. There are 10 seats in the first row, 13 seats in the... (answered by ewatrrr)

An auditorium has 20 seats in the first row, 24 seats in the second row, 28 seats in the... (answered by math_tutor2020,Alan3354)

An auditorium has.7 seats in the first row. 11 seats in the second row.15 seats' I n... (answered by fractalier)

A theater has 37 seats in the first row, 41 seats in the second row, 45 seats in the... (answered by jim_thompson5910)

A theater has 45 seats in the first row, 49 in the second row, 53 seats in the third row... (answered by josmiceli)

Determine the seating capacity of an auditorium with 18 rows of seats if there are 20... (answered by richwmiller)