If 1 = 5, 2 = 25, 3 = 125 then 4 = ?

Appeared in: RML PRE 2025

Explanation

The sequence follows an exponential pattern where each input number 'n' corresponds to 5 raised to the power of 'n' (5ⁿ).
For n=1, the result is 5¹ = 5.
For n=2, the result is 5² = 25.
For n=3, the result is 5³ = 125.
Following this rule, for n=4, the result must be 5⁴, which calculates to 5 × 5 × 5 × 5 = 625.

Option B: This result would be obtained by multiplying the previous term (125) by 4, which breaks the established exponential pattern of using a constant base of 5.
Option C: This number has no discernible mathematical relationship to the established exponential sequence.
Option D: This is the result of 4 raised to the power of 4 (4⁴). The sequence uses a constant base of 5, not a variable base that matches the input number.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Identifying and applying exponential patterns in a number sequence as background academic context rather than a clinical decision trigger.
Pattern recognition is a fundamental cognitive skill essential for data analysis, critical thinking, and problem-solving in many professional fields.
Logical reasoning questions assess the ability to deduce rules from a given set of examples and apply them to find a solution, a skill analogous to diagnosing problems based on a set of symptoms.
What if the sequence was 1=5, 2=10, 3=15? The pattern would be arithmetic (5 × n), and the answer for 4 would be 20, demonstrating the importance of correctly identifying the underlying rule.

How to Approach the Question

First, analyze the relationship between the given pairs of numbers: 1=5, 2=25, 3=125.
Look for a consistent mathematical operation. Test addition, subtraction, multiplication, division, and exponents.
Notice that 25 is 5 × 5 (or 5²) and 125 is 5 × 5 × 5 (or 5³). This strongly suggests an exponential pattern with a base of 5.
Formulate the rule: The output is 5 raised to the power of the input number (5ⁿ).
Apply this rule to the number 4 by calculating 5⁴.
Select the option that matches your calculated result (625).

Concept Tested & Keywords

Concept Tested: Identifying and applying exponential patterns in a number sequence.
Stem keywords: number sequence, pattern, if 1 = 5, 2 = 25, 3 = 125
Lead-in keywords: then 4 = ?

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Practise the full RML PRE 2025

Attempt every question from this paper in a timed mock, then review the full solution for each one.