Question 1206130
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a theater has 20 rows of chairs the first row has 10 chairs and each row after that 
has 2 more seats than the row before it. How many total seats are in the theater?
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<pre>
The series of the chairs in rows is an arithmetic progression.


1-st row has 10 chairs.

The last, 20th row has 10 + (20-1)*2 = 10 + 19*2 = 10 + 38 = 48 chairs.

(use the formula for the n-th term of an AP).



In all, there are  {{{((a[1]+a[20])/2)*20}}} = {{{((10+48)/2)*20}}} = {{{(58/2)*20}}} = 58*10 = 580 chairs.

(use the formula for the sum of the first n terms of an AP).
</pre>

Solved.


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For introductory lessons on arithmetic progressions see 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-arithmetic-progressions.lesson>The proofs of the formulas for arithmetic progressions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-arithmetic-progressions.lesson>Problems on arithmetic progressions</A>  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-arithmetic-progressions.lesson>Word problems on arithmetic progressions</A>

in this site.