In a geometric progression, each number is related to the preceding one by the same ratio. Which sequence is an example of a geometric progression? A. 4, 12, 36 B. 3, 21, 35 C. 1, 2, 3 D. 4, 6, 8

A geometric progression (also known as a geometric sequence) is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. To determine if a sequence is a geometric progression, you can divide each term by the preceding term. If the ratio is the same for all consecutive terms, it is a geometric progression.

Now, let's check each of the sequences given:

A. 4, 12, 36 To check this sequence, we'll divide the second term by the first term and the third term by the second term: 12 ÷ 4 = 3 36 ÷ 12 = 3 The ratio is the same for all consecutive terms (which is 3), so sequence A is a geometric progression.

B. 3, 21, 35 Let's check the ratio: 21 ÷ 3 = 7 35 ÷ 21 ≈ 1.666 The ratio is not the same (7 is not equal to 1.666), so sequence B is not a geometric progression.

C. 1, 2, 3 Check the ratio here: 2 ÷ 1 = 2 3 ÷ 2 = 1.5 The ratios are different, so sequence C is not a geometric progression.

D. 4, 6, 8 Checking the ratios: 6 ÷ 4 = 1.5 8 ÷ 6 ≈ 1.333 Again, the ratios are different, which means sequence D is not a geometric progression.

Therefore, the sequence that is an example of a geometric progression is A. 4, 12, 36.