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Question

Difficulty: MediumNumber and Alphabet Series
Consider the following numerical sequence:
3,11,38,102,227,…3, 11, 38, 102, 227, \dots
What is the value of the next term in this sequence?

Answer: 443

Answer

The next term in the sequence is 443.
Each term increases by the cube of consecutive natural numbers starting from 2: +2³, +3³, +4³, +5³, and +6³. Adding 6³ (which equals 216) to the preceding term 227 yields 443.

Step-by-Step Solution

1
Find the difference between consecutive terms in the given sequence.
The differences are 8, 27, 64, and 125.
Analyzing first-order differences reveals the rate of increase between terms.
2
Identify the logical pattern governing the sequence of differences.
The differences correspond to consecutive perfect cubes: 2³, 3³, 4³, and 5³.
Recognizing that 8 = 2³, 27 = 3³, 64 = 4³, and 125 = 5³ establishes the cubic growth rule.
3
Calculate the next term by extending the identified pattern.
Next difference = 6³ = 216, resulting in next term = 227 + 216 = 443.
Following the consecutive cubic sequence, the fifth difference must be 6³.

Key Concept

Cube-Difference Series Progression
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Topics

Number and Alphabet Series

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