document.write( "Question 553900: decide whether the sequence is arithmetic, geometric, or neither. Explain your answer.\r
\n" ); document.write( "\n" ); document.write( "24. 6, 24, 96, 384...
\n" ); document.write( "25. 1,3,7,13...
\n" ); document.write( "26. 4, 13, 22, 31...
\n" ); document.write( "27. 3, -1, -5, -9...
\n" ); document.write( "28. -11, -7, -3, 1...
\n" ); document.write( "29. 1/2, 3/2, 9/2, 27/2...
\n" ); document.write( "30. 1/3, 2/3, 1, 4/3...
\n" ); document.write( "31. -3/4, 1/8, -1/16, 3/32...
\n" ); document.write( "32. -3/5, 4/25, 5/125, 6/625...\r
\n" ); document.write( "\n" ); document.write( "find the common ratio of the geometric sequence\r
\n" ); document.write( "\n" ); document.write( "33. 1,4,16,64...
\n" ); document.write( "34. 3,6,12,24...
\n" ); document.write( "35. -3,6,-12, 24...
\n" ); document.write( "36. 5,40,320,2560...
\n" ); document.write( "37. 136,68,34,17...
\n" ); document.write( "38. -1/4,1/8, -1/16,1/32...\r
\n" ); document.write( "\n" ); document.write( "write a rule for the nth term of the geometric sequence. then fina a6.\r
\n" ); document.write( "\n" ); document.write( "39. 1,-4,16,-64...
\n" ); document.write( "40. 5,10,20,40...
\n" ); document.write( "41. 2,14,98,686
\n" ); document.write( "42. 6,-30,150,-750...
\n" ); document.write( "43. 5,-5/3,5/9,-5/27...
\n" ); document.write( "44. 2,4/3,8/9,16/27\r
\n" ); document.write( "\n" ); document.write( "please show ur work,, thanks for ur help!
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Algebra.Com's Answer #361148 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
24. 6, 24, 96, 384...
\n" ); document.write( "The differences between consecutive terms are not the same, so it's not an arithmetic sequence:
\n" ); document.write( "\"24-6=18\", \"96-24=72\"
\n" ); document.write( "The ratio of consecutive terms is constant:
\n" ); document.write( "\"24%2F6\" = \"96%2F24\" = \"384%2F96\" = \"4\" So it is a geometric sequence with common ratio = 4.
\n" ); document.write( "25. 1,3,7,13... has neither common difference, nor common ratio
\n" ); document.write( "\"3-1=2\", \"7-3=4\", \"13-7=6\" --> not an arithmetic sequence
\n" ); document.write( "\"3%2F1=3\", \"7%2F3=7%2F3\", \"13%2F7=13%2F7\" --> not a geometric sequence
\n" ); document.write( "26. 4, 13, 22, 31...
\n" ); document.write( "\"13-4=22-13=31-33=9\" ---> arithmetic sequence
\n" ); document.write( "27. 3, -1, -5, -9...
\n" ); document.write( "\"-1-%283%291=-1-3=-4\", \"-5-%28-1%29=-5%2B1=-4\", \"-9-%28-5%29=-9%2B5=-4\" --> arithmetic sequence
\n" ); document.write( "28. -11, -7, -3, 1...
\n" ); document.write( "\"-7-%28-11%291=-7%2B11=4\", \"-3-%28-7%29=-3%2B7=4\", \"1-%28-3%29=1%2B3=4\" --> arithmetic sequence
\n" ); document.write( "29. 1/2, 3/2, 9/2, 27/2...
\n" ); document.write( "\"%281%2F2%29%2F%283%2F2%29\" = \"%289%2F2%29%2F%283%2F2%29\" = \"%2827%2F2%29%2F%289%2F2%29\" = \"3\" --> geometric sequence
\n" ); document.write( "30. 1/3, 2/3, 1, 4/3...
\n" ); document.write( "\"2%2F3-%281%2F3%29=1-%282%2F3%29=4%2F3-1=1%2F3\" --> arithmetic sequence
\n" ); document.write( "31. -3/4, 1/8, -1/16, 3/32...
\n" ); document.write( "the numbers alternate between positive and negative, and so will the difference, so there cannot be a common difference --> not an arithmetic sequence
\n" ); document.write( "\"%281%2F8%29%2F%28-3%2F4%29=-1%2F6\", \"%28-1%2F16%29%2F%281%2F8%29=-1%2F2\", \"%283%2F32%29%2F%28-1%2F16%29=-3%2F2\" --> not a geometric sequence
\n" ); document.write( "32. -3/5, 4/25, 5/125, 6/625...
\n" ); document.write( "\"4%2F25-%28-3%2F5%29=4%2F25%2B15%2F25=19%2F25\", \"5%2F125-4%2F25=5%2F125-20%2F125=-15%2F125=-3%2F25\", \"6%2F625-5%2F125=6%2F625-25%2F625=-19%2F625\" --> not an arithmetic sequence
\n" ); document.write( "\"%284%2F25%29%2F%28-3%2F5%29=-%284%2F25%29%285%2F3%29=-4%2F15\", \"%285%2F125%29%2F%284%2F25%29=%285%2F125%29%2A%2825%2F4%29=1%2F4\", \"%286%2F625%29%2F%285%2F125%29=%286%2F625%29%2A%28125%2F5%29=6%2F25\" --> not a geometric sequence
\n" ); document.write( "find the common ratio of the geometric sequence
\n" ); document.write( "33. 1,4,16,64...
\n" ); document.write( "\"4%2F1=16%2F4=64%2F16=4\" The common ratio is 4.
\n" ); document.write( "34. 3,6,12,24...
\n" ); document.write( "\"6%2F3=12%2F6=24%2F12=2\" The common ratio is 2.
\n" ); document.write( "35. -3,6,-12, 24...
\n" ); document.write( "\"6%2F%28-3%29=%28-12%29%2F6=24%2F%28-12%29=-2\" The common ratio is -2.
\n" ); document.write( "36. 5,40,320,2560... You can do this one.
\n" ); document.write( "37. 136,68,34,17... You can do this one.
\n" ); document.write( "38. -1/4,1/8, -1/16,1/32...
\n" ); document.write( "\"%281%2F8%29%2F%28-1%2F4%29=-%281%2F8%29%284%2F1%29=-1%2F2\", \"%28-1%2F16%29%2F%281%2F8%29=-%281%2F16%29%288%2F1%29=-1%2F2\",
\n" ); document.write( "\"%281%2F32%29%2F%28-1%2F16%29=-%281%2F32%29%2816%2F1%29=-1%2F2\" The common ratio is -1/2.
\n" ); document.write( "write a rule for the nth term of the geometric sequence. Then find \"a%5B6%5D\".
\n" ); document.write( "39. 1,-4,16,-64...
\n" ); document.write( "First find the common ratio and first term:
\n" ); document.write( "\"%28-4%29%2F1=-4\" The common ratio is \"r=-4\"
\n" ); document.write( "The first term is \"a%5B1%5D=1\".
\n" ); document.write( "\"a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29\" ---> \"a%5Bn%5D=1%2A%28-4%29%5E%28n-1%29\"
\n" ); document.write( "\"a%5B6%5D=1%2A%28-4%29%5E%286-1%29=1%2A%28-4%29%5E5=1%2A-1024=-1024\"
\n" ); document.write( "40. 5,10,20,40... \"a%5B1%5D=5\", \"r=10%2F5=2\"
\n" ); document.write( "\"a%5Bn%5D=5%2A2%5E%28n-1%29\"
\n" ); document.write( "\"a%5B6%5D=5%2A2%5E%286-1%29=5%2A2%5E5=5%2A32=160\"
\n" ); document.write( "41. 2,14,98,686 You can do this one.
\n" ); document.write( "42. 6,-30,150,-750... You can do this one.
\n" ); document.write( "43. 5,-5/3,5/9,-5/27... \"a%5B1%5D=5\", \"r=5%2F%28-5%2F3%29=-%285%29%2A%283%2F5%29=-1%2F3\"
\n" ); document.write( "\"a%5Bn%5D=5%2A%28-1%2F3%29%5E%28n-1%29\"
\n" ); document.write( "\"a%5B6%5D=5%2A%28-1%2F3%29%5E%286-1%29=5%2A%28-1%2F3%29%5E5=5%2A%28-1%2F243%29=-5%2F243\"
\n" ); document.write( "44. 2,4/3,8/9,16/27 \"a%5B1%5D=2\", \"r=%284%2F3%29%2F2=%284%2F3%29%2A%281%2F2%29=2%2F3\"
\n" ); document.write( "\"a%5Bn%5D=2%2A%282%2F3%29%5E%28n-1%29\"
\n" ); document.write( "\"a%5B6%5D=2%2A%282%2F3%29%5E%286-1%29=2%2A%282%2F3%29%5E5=2%2A%2832%2F243%29=64%2F243\"
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