It is observed that in each case, every term except the first term bears a constant ratio to the term immediately preceding it. Such sequences are called:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Geometric Progression
A geometric progression (GP) is a sequence in which each term after the first is got by multiplying the term before it by a fixed number, the common ratio. So every term bears a constant ratio to the term just before it, for example 3, 6, 12, 24, ... (ratio 2).
Why the other options are incorrect
Option (1) Arithmetic Progression — Incorrect. In an AP each term differs from the one before by a constant difference, not a constant ratio (3, 6, 9, 12, ...).
Option (3) Harmonic Progression — Incorrect. In an HP the reciprocals of the terms form an AP (1, 1/2, 1/3, 1/4, ...).
Option (4) Arithmetic cum Geometric Progression — Incorrect. Its terms are products of an AP term and a GP term (1, 2x, 3x2, ...), so the ratio between terms is not constant.