SOLUTION: decide whether the sequence is arithmetic, geometric, or neither. Explain your answer. 24. 6, 24, 96, 384... 25. 1,3,7,13... 26. 4, 13, 22, 31... 27. 3, -1, -5, -9... 28. -1

Algebra ->  Inverses -> SOLUTION: decide whether the sequence is arithmetic, geometric, or neither. Explain your answer. 24. 6, 24, 96, 384... 25. 1,3,7,13... 26. 4, 13, 22, 31... 27. 3, -1, -5, -9... 28. -1      Log On


   

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