Which of the following list of numbers is/are in Geometric Progressions?
(A) 6, 12, 24, 48...
(B) 2, 6, 18, 20...
(C) 3, 9, 27, 81...
(D) 4, 12, 36...
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (C) and (D) only
A list is a geometric progression when each term is the previous term multiplied by the same number (the common ratio), so the ratio of every term to the one before it must be equal.
(A) 6, 12, 24, 48... Correct. Each term is twice the one before (12 ÷ 6, 24 ÷ 12 and 48 ÷ 24 all give 2).
(B) 2, 6, 18, 20... Incorrect. The ratios are 3 and 3, but \(\frac{20}{18}\) is not 3, so the ratio breaks at the fourth term (a GP would need 54).
(C) 3, 9, 27, 81... Correct. Each term is three times the one before.
(D) 4, 12, 36... Correct. Each term is three times the one before (12 ÷ 4 and 36 ÷ 12 both give 3).