Which of the following lists of numbers is/are a Geometric Progression:
(A) 2, 4, 8, 16, 32,........
(B) 3, 9, 27, 81,.......
(C) −3, −6, −12, −24,.......
(D) 21, 18, 15,.......
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (C) only
A Geometric Progression is a list in which each term is the previous term multiplied by the same number (the common ratio), so the ratio of any term to the one before it never changes.
(A) 2, 4, 8, 16, 32, ... Correct. Each term is twice the one before it: \(\frac{4}{2}=\frac{8}{4}=\frac{16}{8}=2\), a common ratio of 2.
(B) 3, 9, 27, 81, ... Correct. Each term is three times the one before it, a common ratio of 3.
(C) −3, −6, −12, −24, ... Correct. \(\frac{-6}{-3}=\frac{-12}{-6}=\frac{-24}{-12}=2\); negative terms do not matter, the common ratio is 2.
(D) 21, 18, 15, ... Incorrect. Here \(\frac{18}{21}\ne\frac{15}{18}\), so there is no common ratio; each term is 3 less than the one before, which makes it an Arithmetic Progression.