Mathematics

Mathematics

Problem

Consider the set of all positive multiples of 99. When these numbers are written in ascending order, which statement correctly classifies the sequence? a) Finite AP because there is a largest multiple of 99 b) Infinite GP because each term can be written as 9×2n9\times 2^n c) Infinite AP because the multiples continue without end d) Not an AP because the terms are unevenly spaced
Intuitive explanation

The key insight is recognizing that positive multiples of 9 form a sequence where each term follows a predictable pattern: 9,18,27,36,…9, 18, 27, 36, \ldots or 9⋅1,9⋅2,9⋅3,9⋅4,…9 \cdot 1, 9 \cdot 2, 9 \cdot 3, 9 \cdot 4, \ldots The difference between consecutive terms is always constant (always 9), which is the defining feature of an arithmetic sequence. Once you spot that constant difference, you've identified the sequence type and can predict any term without listing them all.

Intuitive explanation

The key insight is recognizing that positive multiples of 9 form a sequence where each term follows a predictable pattern: 9,18,27,36,…9, 18, 27, 36, \ldots or 9⋅1,9⋅2,9⋅3,9⋅4,…9 \cdot 1, 9 \cdot 2, 9 \cdot 3, 9 \cdot 4, \ldots The difference between consecutive terms is always constant (always 9), which is the defining feature of an arithmetic sequence. Once you spot that constant difference, you've identified the sequence type and can predict any term without listing them all.

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