Option C
-3, 3 -3, 3,-3 ,3 is a geometric sequence
Solution:
Given that, we have to find the geometric sequence
A geometric sequence is a sequence in which the ratio of any term to the previous term is constant
Option A
0, -3, -6, -9, -12 ,-15,
Find the common ratio
[tex]r = \frac{-3}{0}\\\\r = \frac{-6}{-3} = 2[/tex]
Thus common ratio is not constant
Therefore, this is not a geometric sequence
Option B
-2, 0, 2, 4, 6,
Find the common ratio
[tex]r = \frac{0}{-2} = 0\\\\r = \frac{2}{0}[/tex]
Thus common ratio is not constant
Therefore, this is not a geometric sequence
Option C
-3, 3 -3, 3,-3 ,3
Find the common ratio
[tex]r = \frac{3}{-3} = -1\\\\r = \frac{-3}{3} = -1\\\\r = \frac{3}{-3} = -1\\\\r = \frac{-3}{3} = -1[/tex]
Thus common ratio is constant
Therefore, it is a geometric sequence
Option D
5, 7, 9, 11 ,13
Find the common ratio
[tex]r = \frac{7}{5} = 1.4\\\\r = \frac{9}{7} = 1.28\\\\r = \frac{11}{9} = 1.22[/tex]
Thus common ratio is not constant
Therefore, this is not a geometric sequence
