document.write( "Question 764815: Can someone Please help me solve this problem, Thank You very much!!!\r
\n" ); document.write( "\n" ); document.write( "A theater has 41 seats in the first row, 43 seats in the second row, 45 seats in the third row, and so on.\r
\n" ); document.write( "\n" ); document.write( "(a) Can the number of seats in each row be modeled by an arithmetic or gemetric sequence?
\n" ); document.write( "(b) Write the general term for a sequence a^n that gives teh number of seats in row n.
\n" ); document.write( "(c) How many seats are there in row 20?\r
\n" ); document.write( "\n" ); document.write( "(a) what type of sequence is present?
\n" ); document.write( "--Geometric
\n" ); document.write( "--Arithmetic\r
\n" ); document.write( "\n" ); document.write( "(b)a^n=___\r
\n" ); document.write( "\n" ); document.write( "(c) There are __ seats in row 20.\r
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Algebra.Com's Answer #465772 by ramkikk66(644) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Your question:\r\n" );
document.write( "A theater has 41 seats in the first row, 43 seats in the second row, 45 seats in the third row, and so on.\r\n" );
document.write( "(a) Can the number of seats in each row be modeled by an arithmetic or gemetric sequence?\r\n" );
document.write( "(b) Write the general term for a sequence a^n that gives teh number of seats in row n.\r\n" );
document.write( "(c) How many seats are there in row 20? \r\n" );
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document.write( "Solution:\r\n" );
document.write( "a) The difference between the number of seats in consecutive rows is a constant,\r\n" );
document.write( "so it is an ARITHMETIC progression. (A geometric progression is one where the\r\n" );
document.write( "ratio of adjacent terms is a constant. E.g. 2,4,8,16...)\r\n" );
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document.write( "b) \r\n" );
document.write( "n = 1, row 1, number of seats = 41\r\n" );
document.write( "n = 2, row 2, number of seats = 43 = 41 + 2*1 = 41 + d*1 (where d = 2)\r\n" );
document.write( "n = 3, row 3, number of seats = 45 = 41 + 2*2 = 41 + d*2 (where d = 2)\r\n" );
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document.write( "So if we call the first term as a (which is 41 here), and d as the common\r\n" );
document.write( "difference between 2 terms (which is 2 here), the nth term is\r\n" );
document.write( "a + (n-1)*d\r\n" );
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document.write( "This is the general formula for the nth term in any arithmetic progression\r\n" );
document.write( "with the first term as a, and common difference as d.\r\n" );
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document.write( "So number of seats in row n = \r\n" );
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document.write( "3) How many seats in row 20? Simple - substitute n = 20 in the above formula\r\n" );
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document.write( "Row 20 has  seats\r\n" );
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document.write( "Hope you got it :)\r\n" );
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