document.write( "Question 815181: Dear Team\r
\n" ); document.write( "\n" ); document.write( "can you please help to get answers on these 2 questions?\r
\n" ); document.write( "\n" ); document.write( "1.Select the option for “?” that continues the pattern in each question
\n" ); document.write( "2, 7, 26, 101, 400, ?\r
\n" ); document.write( "\n" ); document.write( "2.Select the option for “?” that continues the pattern in each question
\n" ); document.write( "7, 21, 8, 72, 9, ? \n" ); document.write( "
Algebra.Com's Answer #490756 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "2, 7, 26, 101, 400, ?\r\n" );
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document.write( "It's not a geometric sequence, but it goes up fast like \r\n" );
document.write( "one, so let's see how close it is to one.\r\n" );
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document.write( "The ratios of each term to the preceding one are\r\n" );
document.write( "7/2 = 3.5\r\n" );
document.write( "26/7 = 3.714\r\n" );
document.write( "101/26 = 3.885\r\n" );
document.write( "400/101 = 3.960\r\n" );
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document.write( "Those ratios seem to be getting close to 4.\r\n" );
document.write( "So let's investigate how close each term is to \r\n" );
document.write( "being 4 times the preceding term\r\n" );
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document.write( "Term #1:  7 is close to 4×2 which is 8.  It's just 1 less.\r\n" );
document.write( "Term #2:  26 is close to 4×7 which is 28.  It's just 2 less.\r\n" );
document.write( "Term #3:  101 is close to 4×26 which is 104.  It's just 3 less.\r\n" );
document.write( "Term #4:  400 is close to 4×101 which is 404.  It's just 4 less.\r\n" );
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document.write( "Aha.  Now we see the pattern.\r\n" );
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document.write( "Each term is 4 times the preceding term minus the number of term.\r\n" );
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document.write( "So term #5 will be 4×400 = 1600. Then 1600-5 (the term number) = 1595\r\n" );
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document.write( "7, 21, 8, 72, 9\r\n" );
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document.write( "It looks like the odd terms have the pattern 7,8,9,10,11,...\r\n" );
document.write( "Term #1 is 7\r\n" );
document.write( "Term #2 is 21 or 7×31, and 1 is half of 2, the term number \r\n" );
document.write( "Term #3 is 8\r\n" );
document.write( "Term #4 is 72 or 8×9 or 8×3², and 2 is half of 4, the term number\r\n" );
document.write( "Term #5 is 9\r\n" );
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document.write( "So each odd term is the next term of 7,8,9,10,11,...\r\n" );
document.write( "Then each even term is the preceding odd term times\r\n" );
document.write( "3 raised to the power which is half the term number. \r\n" );
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document.write( "So term #6 is 9×3³ since 3 is half the term number 6, \r\n" );
document.write( "and 9×3³ = 9×27 = 243.\r\n" );
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document.write( "Edwin
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