Question

Determine if the sequence is geometric. If it is, find the common ratio.

1) -2, 2/3, -2/9, 2/27
2) 0,2,5,9
3) 2, -10, 50, -250
4) 1,4,16,64

Answer 1

1. -1/3
2. not geometric
3. -5
4. 4

Explanation:

You find the ratio of terms by dividing the second by the first. If the ratio is the same for all adjacent pairs of terms, it is a "common" ratio.

1) (2/3)/-2 = -1/3

(-2/9)/(2/3) = -1/3

(2/27)/(-2/9) = -1/3 . . . . . the common ratio is -1/3

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2) 2/0 = undefined . . . . not a geometric sequence

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3) -10/2 = -5

50/-10 = -5

-250/50 = -5 . . . . . the common ratio is -5

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4) 4/1 = 4

16/4 = 4

64/16 = 4 . . . . . the common ratio is 4