<p>In a theater, the front row has 30 seats. each row behind the first row has 4 more seats than the row in front of it. if there are 26 rows, what is the total number of seats in the theater?</p>
<p>Barron's has the answer 2080, but the explanation is crap and doesn't tell you why it multiplies certain numbers to get the number. Anyone want to explain this step, by step for me?</p>
<p>Also is there any secret to doing the distance problems quickly. The one's that have a box divided into 9 squares and it asks you how many ways you can get to a certain point, etc? tracing them and counting them one by one is too slow...</p>
<p>For the theater question I believe you can use this:
Ssubn = (n/2)(Asub1+AsubN)
Ssubn = sum of n terms
N = Number of terms
Asub1 = first term
AsubN = last term
so you have Ssubn = (26/2)(30+AsubN)
AsubN = Asub1 + (n-1)d
d = the rate of increase, 4
n = the nth term, you want to find the 26th term in the sequence
Asub1 = first term, 30
AsubN = 30 + 25<em>4
AsubN = 130
SsubN = (26/2)(30+130)
SsubN = 13</em>160 or 2080</p>
<p>In the back of the Barron’s book on page 366, there are many formulas. The 11th one gives you the answer(nth term=26, common difference=4, first term=30). Just know those formulas. If you don’t want to memorize them, put them into your graphing calculator(programs).</p>
<p>edit: kysuke got it before me. I gave him a page reference for the book, and it would definitely be a good idea to have those formulas down in some sort of way.</p>
<p>I don’t know of any rules that say you can’t have formulas in there. They just don’t want advanced calculators that are practically like computers.</p>
If the question says every move you make must be closer to the destination (as in, you aren’t allowed to move backwards/backtrack), then you can use the idea of Pascal’s Triangle and permutations.</p>