document.write( "Question 301233: 8, a, 14, b, 20,…..\r
\n" ); document.write( "\n" ); document.write( "the first term of the sequence above is 8. Which of the following could be the formula for finding the nth term of this sequence for any positive integer n ?\r
\n" ); document.write( "\n" ); document.write( "a 2n+6 b 3n+5 c 5n+3 d 6n+2 e 6n+5 \r
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Algebra.Com's Answer #215989 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
8, a, 14, b, 20,…..
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document.write( "Hmmm?  Are you talking about this sequence:\r\n" );
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document.write( "8, 14, 20, ...  ?\r\n" );
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document.write( "If so, why did you put the letter \"a\" in between the 8 and the 14, \r\n" );
document.write( "and the letter \"b\" between the 14 and the 20?\r\n" );
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document.write( "But, after looking at the choices given, I think you must be asking\r\n" );
document.write( "about the sequence 8, 14, 20, ... without those letters in between\r\n" );
document.write( "them, right?  I will assume that's what you are asking.\r\n" );
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document.write( "So let's substitute 1, 2, and 3 in each of those choices and see\r\n" );
document.write( "which one gives you all three of those given numbers 8, 14 and 20:   \r\n" );
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document.write( "Let's try choice (a)\r\n" );
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document.write( "  2n+6   \r\n" );
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document.write( "Let's substitute n=1, n=2, and n=3 in 2n+6\r\n" );
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document.write( "2(1)+6 = 2+6 = 8 \r\n" );
document.write( "2(2)+6 = 4+6 = 10\r\n" );
document.write( "2(3)+6 = 6+6 = 12\r\n" );
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document.write( "Therefore, choice (a) is not the correct choice \r\n" );
document.write( "because it gives the sequence\r\n" );
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document.write( "8, 10, 12, ... not the sequence 8, 14, 20, ...\r\n" );
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document.write( "Let's try choice (b)\r\n" );
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document.write( "  3n+5   \r\n" );
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document.write( "Let's substitute n=1, n=2, and n=3 in 3n+5\r\n" );
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document.write( "3(1)+5 = 3+5 = 8 \r\n" );
document.write( "3(2)+5 = 6+5 = 11\r\n" );
document.write( "3(3)+5 = 9+5 = 14\r\n" );
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document.write( "Therefore, choice (b) is not the correct choice \r\n" );
document.write( "because it gives the sequence\r\n" );
document.write( "8, 11, 14, ... not the sequence 8, 14, 20 ... \r\n" );
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document.write( "Let's try choice (c)\r\n" );
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document.write( "  5n+3   \r\n" );
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document.write( "Let's substitute n=1, n=2, and n=3 in 5n+3\r\n" );
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document.write( "5(1)+3 = 5+3 = 8 \r\n" );
document.write( "5(2)+3 = 10+3 = 13\r\n" );
document.write( "5(3)+3 = 15+3 = 18\r\n" );
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document.write( "Therefore, choice (c) is not the correct choice \r\n" );
document.write( "because it gives the sequence\r\n" );
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document.write( "8, 13, 18, ... not the sequence 8, 14, 20 ... \r\n" );
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document.write( "Let's try choice (d)\r\n" );
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document.write( "  6n+2   \r\n" );
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document.write( "Let's substitute n=1, n=2, and n=3 in 6n+2\r\n" );
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document.write( "6(1)+2 = 6+2 = 8 \r\n" );
document.write( "6(2)+2 = 12+2 = 14\r\n" );
document.write( "6(3)+2 = 18+2 = 20\r\n" );
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document.write( "AHA! choice (d) IS the correct choice \r\n" );
document.write( "because it gives the sequence\r\n" );
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document.write( "8, 14, 20, ... \r\n" );
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document.write( "We have found the correct choice to be (d), so we do not really need \r\n" );
document.write( "to try choice (e).  But just for fun let's see why (e) is incorrect, \r\n" );
document.write( "like we did (a), (b) and (c):\r\n" );
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document.write( "Trying choice (e)\r\n" );
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document.write( "  6n+5   \r\n" );
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document.write( "Let's substitute n=1, n=2, and n=3 in 6n+5\r\n" );
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document.write( "6(1)+5 = 6+5 = 11 \r\n" );
document.write( "6(2)+5 = 12+5 = 17\r\n" );
document.write( "6(3)+5 = 18+5 = 23\r\n" );
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document.write( "Therefore, choice (e) is not the correct choice \r\n" );
document.write( "because it gives the sequence\r\n" );
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document.write( "11, 17, 23, ... not the sequence 8, 14, 20 ... \r\n" );
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document.write( "Edwin
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