determining if a sequence is geometric\nwhich sequences are geometric? check all that apply.\n-2, -4, -6…

To determine if a sequence is geometric, we check if there is a common ratio ( r ) such that ( r=\frac{a_{n + 1}}{a_n} ) for all consecutive terms ( a_n ) and ( a_{n+1} ).

Analyzing each sequence:

1. Sequence: (-2,-4,-6,-8,-10,\dots)

   • Calculate the ratio between consecutive terms:
     • ( \frac{-4}{-2} = 2 )
     • ( \frac{-6}{-4} = \frac{3}{2} )
   • Since the ratios are not the same, this sequence is not geometric.

2. Sequence: (16,-8,4,-2,1,\dots)

   • Calculate the ratio between consecutive terms:
     • ( \frac{-8}{16} = -\frac{1}{2} )
     • ( \frac{4}{-8} = -\frac{1}{2} )
     • ( \frac{-2}{4} = -\frac{1}{2} )
     • ( \frac{1}{-2} = -\frac{1}{2} )
   • The common ratio ( r = -\frac{1}{2} ) is consistent, so this sequence is geometric.

3. Sequence: (-15,-18,-21.6,-25.92,-31.104,\dots)

   • Calculate the ratio between consecutive terms:
     • ( \frac{-18}{-15} = 1.2 )
     • ( \frac{-21.6}{-18} = 1.2 )
     • ( \frac{-25.92}{-21.6} = 1.2 )
     • ( \frac{-31.104}{-25.92} = 1.2 )
   • The common ratio ( r = 1.2 ) is consistent, so this sequence is geometric.

4. Sequence: (4,10.5,17,23.5,30,\dots)

   • Calculate the ratio between consecutive terms:
     • ( \frac{10.5}{4} = 2.625 )
     • ( \frac{17}{10.5} \approx 1.619 )
   • Since the ratios are not the same, this sequence is not geometric.

5. Sequence: (625,125,25,5,1,\dots)

   • Calculate the ratio between consecutive terms:
     • ( \frac{125}{625} = \frac{1}{5} )
     • ( \frac{25}{125} = \frac{1}{5} )
     • ( \frac{5}{25} = \frac{1}{5} )
     • ( \frac{1}{5} = \frac{1}{5} )
   • The common ratio ( r=\frac{1}{5} ) is consistent, so this sequence is geometric.

The geometric sequences are:

• ( 16,-8,4,-2,1,\dots )
• ( -15,-18,-21.6,-25.92,-31.104,\dots )
• ( 625,125,25,5,1,\dots )

So the correct options are:
B. ( 16, -8, 4, -2, 1 )
C. ( -15, -18, -21.6, -25.92, -31.104, \dots )
E. ( 625, 125, 25, 5, 1, \dots )