Question 553900
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:
{{{24/6}}} = {{{96/24}}} = {{{384/96}}} = {{{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
{{{3/1=3}}}, {{{7/3=7/3}}}, {{{13/7=13/7}}} --> not a geometric sequence
26. 4, 13, 22, 31...
{{{13-4=22-13=31-33=9}}} ---> arithmetic sequence
27. 3, -1, -5, -9...
{{{-1-(3)1=-1-3=-4}}}, {{{-5-(-1)=-5+1=-4}}}, {{{-9-(-5)=-9+5=-4}}} -->  arithmetic sequence
28. -11, -7, -3, 1...
{{{-7-(-11)1=-7+11=4}}}, {{{-3-(-7)=-3+7=4}}}, {{{1-(-3)=1+3=4}}} -->  arithmetic sequence
29. 1/2, 3/2, 9/2, 27/2...
{{{(1/2)/(3/2)}}} = {{{(9/2)/(3/2)}}} = {{{(27/2)/(9/2)}}} = {{{3}}} -->  geometric sequence
30. 1/3, 2/3, 1, 4/3...
{{{2/3-(1/3)=1-(2/3)=4/3-1=1/3}}} -->  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
{{{(1/8)/(-3/4)=-1/6}}}, {{{(-1/16)/(1/8)=-1/2}}}, {{{(3/32)/(-1/16)=-3/2}}} --> not a geometric sequence
32. -3/5, 4/25, 5/125, 6/625...
{{{4/25-(-3/5)=4/25+15/25=19/25}}}, {{{5/125-4/25=5/125-20/125=-15/125=-3/25}}}, {{{6/625-5/125=6/625-25/625=-19/625}}} --> not an arithmetic sequence
{{{(4/25)/(-3/5)=-(4/25)(5/3)=-4/15}}}, {{{(5/125)/(4/25)=(5/125)*(25/4)=1/4}}}, {{{(6/625)/(5/125)=(6/625)*(125/5)=6/25}}} --> not a geometric sequence
find the common ratio of the geometric sequence 
33. 1,4,16,64...
{{{4/1=16/4=64/16=4}}} The common ratio is 4.
34. 3,6,12,24...
{{{6/3=12/6=24/12=2}}} The common ratio is 2.
35. -3,6,-12, 24...
{{{6/(-3)=(-12)/6=24/(-12)=-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...
{{{(1/8)/(-1/4)=-(1/8)(4/1)=-1/2}}}, {{{(-1/16)/(1/8)=-(1/16)(8/1)=-1/2}}},
{{{(1/32)/(-1/16)=-(1/32)(16/1)=-1/2}}} The common ratio is -1/2.
write a rule for the nth term of the geometric sequence. Then find {{{a[6]}}}. 
39. 1,-4,16,-64...
First find the common ratio and first term:
{{{(-4)/1=-4}}} The common ratio is {{{r=-4}}}
The first term is {{{a[1]=1}}}.
{{{a[n]=a[1]*r^(n-1)}}} ---> {{{a[n]=1*(-4)^(n-1)}}}
{{{a[6]=1*(-4)^(6-1)=1*(-4)^5=1*-1024=-1024}}}
40. 5,10,20,40... {{{a[1]=5}}}, {{{r=10/5=2}}}
{{{a[n]=5*2^(n-1)}}}
{{{a[6]=5*2^(6-1)=5*2^5=5*32=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[1]=5}}}, {{{r=5/(-5/3)=-(5)*(3/5)=-1/3}}}
{{{a[n]=5*(-1/3)^(n-1)}}}
{{{a[6]=5*(-1/3)^(6-1)=5*(-1/3)^5=5*(-1/243)=-5/243}}}
44. 2,4/3,8/9,16/27  {{{a[1]=2}}}, {{{r=(4/3)/2=(4/3)*(1/2)=2/3}}}
{{{a[n]=2*(2/3)^(n-1)}}}
{{{a[6]=2*(2/3)^(6-1)=2*(2/3)^5=2*(32/243)=64/243}}}