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IBM

MCP Math Server

by IBM

geometric_sequence

Generate a geometric sequence by specifying the first term, common ratio, and number of terms for mathematical calculations.

Instructions

Generate a geometric sequence with given first term, common ratio, and number of terms. (Domain: arithmetic, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
first_termYes
common_ratioYes
num_termsYes
Behavior2/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool generates a sequence but does not describe output format (e.g., list of numbers), error handling (e.g., for invalid inputs like negative num_terms), or computational constraints (e.g., limits on term size). This leaves significant gaps for a tool with three parameters and no output schema.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is concise and front-loaded in a single sentence, with no wasted words. The parenthetical note about domain and category is brief and does not detract from clarity. However, it could be slightly more structured by separating usage notes from the core purpose.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's complexity (three parameters, no annotations, no output schema), the description is incomplete. It lacks details on output format, error conditions, and example usage, which are crucial for an agent to invoke it correctly. The domain/category hint is insufficient to compensate for these gaps.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters2/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has 0% description coverage, and the tool description only lists parameter names ('first term, common ratio, and number of terms') without explaining their semantics, units, or valid ranges. For example, it doesn't clarify if 'num_terms' must be positive or if 'common_ratio' can be zero. This adds minimal value beyond the schema's property names.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose: 'Generate a geometric sequence with given first term, common ratio, and number of terms.' It specifies the verb ('generate'), resource ('geometric sequence'), and required inputs. However, it does not explicitly differentiate from sibling tools like 'geometric_series' or 'geometric_sum', which are related but distinct operations, so it falls short of a perfect score.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('general'), but this is too vague to help an agent choose between similar tools like 'geometric_series' or 'arithmetic_sequence'. There are no explicit instructions on use cases, prerequisites, or exclusions.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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