Question

An auditorium has 25 rows of seats. Row 1 contains 12 seats. Each additional row contains two more seats than the previous row. What is the total number of seats in the auditorium?

Answer 1

Answer: There is a total of 900 seats in the auditorium.

Explanation:

there is a formula for this

t - n = a + ( n - 1) d

It is called a Arithmetic Progression.

We use this to find the number of seats in the last row first.

a = initial value, 12

d = common difference for each successive term

n = is the number of terms in the sequence

t - 25 = 12 + (25 -1) * 2

We ignore the left side for now, just solve the right and we get 60.

Now we use the equation,

n / 2 (2a + n -1 * d)

So,

25/2 ( 24 + 24 * d)

The answer is 900