# Thread: Easy Question... find the equation...

1. ## Easy Question... find the equation...

I forgot how to do this...

Determine the seating capacity of an auditorium with 30 rows of seats if there are 25 seats in the first row, 28 seats in the second row, 31 seats in the third row, 34 seats in the forth row, and so on.

I don't want the answer... I need to build the equation.

This is what I've done so far:

Each row increases by three seats.

So, for 30 rows... 30 • 3 = 90, right? There are 90 additional seats...

So.. is it 25 + 90?

2. Originally Posted by Polyxendi
I forgot how to do this...

Determine the seating capacity of an auditorium with 30 rows of seats if there are 25 seats in the first row, 28 seats in the second row, 31 seats in the third row, 34 seats in the forth row, and so on.

So.. is it 25 + 90? does that sound reasonable based on the above statement?
you need these two formulas ...

$\displaystyle a_n = a_1 + (n-1)d$

$\displaystyle S_n = \frac{n}{2}(a_1 + a_n)$

3. You can use $\displaystyle S_n = \frac{n}{2}[2a+(n-1)]\times d$

In your case a= 25, d= 3 and n= 30