Shortcut Trick
The series follows a multiplication pattern with factors increasing by 0.5 each time.
Pattern: ×0.5, ×1, ×1.5, ×2, ×2.5
Missing term = 1.5 × 2 = 3
Check: 3 × 2.5 = 7.5 (Matches the last term)
∴ The correct answer is 3.
Alternate Method
Given Series: 2, 1, 1, 1.5, ?, 7.5
2 ×0.5 → 1 ×1.0 → 1 ×1.5 → 1.5 ×2.0 → 3 ×2.5 → 7.5
The logic of the series is multiplying each term by an arithmetic progression (0.5, 1.0, 1.5, 2.0, 2.5...).
⇒ 2 × 0.5 = 1
⇒ 1 × 1.0 = 1
⇒ 1 × 1.5 = 1.5
⇒ 1.5 × 2.0 = 3
⇒ 3 × 2.5 = 7.5
∴ The correct answer is 3.
Additional Information
Multiplication Series
In this type, each term is multiplied by a fixed or a varying number to get the next term. Common varying factors include AP (0.5, 1, 1.5...) or squares/cubes.
Decimal Multiplication Pattern
Often used in exams, this pattern usually starts with ×0.5 or ×1.5, resulting in numbers decreasing once then increasing rapidly.
Arithmetic-Geometric Series
A complex series where both addition and multiplication (or division) occur in a single step, such as (n × 1) + 1, (n × 2) + 2, etc.