document.write( "Question 953582: An amphitheater has 22 seats in the first row and 40 rows in all. Each successive row has one additional seat. How many seats are in the amphitheater?\r
\n" ); document.write( "\n" ); document.write( "I believe 1660 seats but I did a long explanation of this and don't know a way to find it easier I made a list adding one to every number for 40 rows excluding the first one. \n" ); document.write( "
Algebra.Com's Answer #582371 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
i believe this is an arithmetic progression.
\n" ); document.write( "the formula for the sum of an arithmetic progression is:
\n" ); document.write( "Sn = n*(A1+An)/2
\n" ); document.write( "For example:
\n" ); document.write( "If you have the arithmetic progression 1,2,3,4,5, then the sum is 15.
\n" ); document.write( "The formula would be:
\n" ); document.write( "Sn = 5 * (1 + 5)/2 = 5 * 6/2 = 5 * 3 = 15.
\n" ); document.write( "The formula will get you the sum without all the tears.
\n" ); document.write( "Sometimes you have to find An first.
\n" ); document.write( "The formula for that is:
\n" ); document.write( "An = A1 + (n-1) * d
\n" ); document.write( "d is the common difference.
\n" ); document.write( "In case you didn't figure it out by now:
\n" ); document.write( "A1 is the first term in the series.
\n" ); document.write( "An is the nth term in the series.
\n" ); document.write( "n is the number of terms in the series.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's apply these formulas to your problem:
\n" ); document.write( "Your first row is 22 seats, so A1 = 22.
\n" ); document.write( "Each succeeding row has 1 more seat, so d = 1.
\n" ); document.write( "There are 40 rows in all, so n = 40\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "First we have to find An.
\n" ); document.write( "Then we can find Sn.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "An = A1 + (n-1) * d.
\n" ); document.write( "replace A1 with 22 n with 40 and d with 1 and the formula becomes:
\n" ); document.write( "An = 22 + 39 * 1 = 22 + 39 = 61.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Sn = n * (A1 + An) / 2.
\n" ); document.write( "replace n with 40 and A1 with 22 and An with 61 and the formula becomes:
\n" ); document.write( "Sn = 40 * (22 + 61) / 2 = 40 * 83/2 = 40 * 41.5 = 1660\r
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\n" ); document.write( "\n" ); document.write( "You got the right answer.
\n" ); document.write( "The sum is 1660.
\n" ); document.write( "The formulas, if you remember them, make the job a lot easiwer.\r
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\n" ); document.write( "\n" ); document.write( "The formulas are, once again:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "An = A1 * (n-1)*d\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Sn = n * (A1 + An) / 2\r
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\n" ); document.write( "\n" ); document.write( "Here's some good links for future reference:\r
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\n" ); document.write( "\n" ); document.write( "http://www.regentsprep.org/regents/math/algtrig/atp2/arithseq.htm\r
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\n" ); document.write( "\n" ); document.write( "http://www.regentsprep.org/regents/math/algtrig/atp2/geoseq.htm\r
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