Which of the following is a geometric series? a. 40 + 50 + 60 + 70 b. 40 + 42 + 44 + 46 c. 40 + 80 + 40 + 120 d. 40 + 20 + 10 + 5

40 + 20 + 10 + 5 is a geometric series.

Step-by-step explanation:

in a geometric series the ratio of consecutive terms is equal and the ratio is called the common ratio of the geometric series.

Let us find the ratio of consecutive terms of each of the given series.

For the series 40 + 50 + 60 + 70

50/40 = 5/4

60/50 = 6/5

Since, 5/4 ≠ 6/5 hence, it is not a geometric series.

For the series 40 + 42 + 44 + 46

42/40 = 21/10

44/42 = 22/21

Since, 21/10 ≠ 22/21 hence, it is not a geometric series.

For the series 40 + 80 + 40 + 120

80/40 = 2

40/80 = 1/2

Since, 2 ≠ 1/2 hence, it is not a geometric series.

For the series 40 + 20 + 10 + 5

20/40 = 1/2

10/20 = 1/2

Since, 1/2 = 1/2 hence, it is a geometric series.

Therefore, D is the correct option.

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