An auditorium has 25 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?

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msanchez4317 msanchez4317

Today at 4:12 PM
Mathematics

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An auditorium has 25 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?

Answer :

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destiny111263 destiny111263 · Answer 1 · 2025-03-23T16:17:17-04:00

destiny111263 destiny111263

Today at 4:17 PM

Answer:

there are 50 seats in the auditorium

Step-by-step explanation:

There are 25 rows and the seats are counting up by 2 then you multiply 25 times 2 and you would get 50 seats

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keshavgandhi04 keshavgandhi04 · Answer 2 · 2025-03-23T16:17:17-04:00

The total seats in the auditorium will total 850 seats.

What is Arithmetic progression?

The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).

The arithmetic progression has wider use in mathematics for example sum of natural numbers.

Natural number = 1,2,3,4,5,6,7,8...

Now it has the same difference between any two consecutive terms d =2-1 = 3-2 .

Given,

Seats in first raw = 10

Seats in second raw = 12

Seats in third raw = 14 and so on

So.

Series 10, 12, 14, .... is an arithmetic progression series

First term a = 10

Common difference (d) = 12 - 10 = 2

Number of terms (n) = 25

The Sum of arithmetic series is given by

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

So,

S = 25/2[2×10 + (25 - 1)2]

S = 25/2[20 + 48]

S = 25/2(68)

S = 850

Hence, The total seats in the auditorium will total 850 seats.

For more about Arithmetic progression,

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