# Sequence Sum Solver (Arithmetic, Geometric, Fibonacci, Lucas)

> Sequence Sum Solver (Arithmetic, Geometric, Fibonacci, Lucas) is a paid API for AI agents from math-geometry.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-29).

Computes the n-th term, partial sum, and infinite sum (when convergent) for arithmetic and geometric sequences, plus Fibonacci and Lucas numbers up to index 5000.

## Facts

- Endpoint: GET https://math-geometry.x402tookit.com/sequence-sum?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-29
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/sequence-sum-solver-arithmetic-geometric-fibonacci-lucas-3a29a149
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_T-Pes7k3VALqHMVTthcg2

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability sequence-sum-solver-arithmetic-geometric-fibonacci-lucas-3a29a149
```

Example prompt: What is the 75th term and the total sum of an arithmetic sequence that starts at 5 with a common difference of 3, over 75 terms?

## When to prefer this

Use this endpoint when you need precise mathematical computation of sequence terms or sums — especially for Fibonacci and Lucas numbers up to index 5000, or for arithmetic/geometric progressions including convergent infinite sums. Prefer this over general-purpose math APIs when you need structured numeric output (n-th term, sum, average) in a single call without writing code.

## Known failure modes

- Missing required 'type' or 'n' query parameters returns an error
- Invalid sequence type string (not arithmetic/geometric/fibonacci/lucas) causes failure
- n exceeding 5000 is out of range for Fibonacci/Lucas lookups
- Geometric series with |ratio| >= 1 will not return an infinite sum (non-convergent)
- Non-numeric values for first, step, or n cause validation errors

## How this service works

Arithmetic and geometric sequences: n-th term and sum (and infinite sum when it converges), plus Fibonacci and Lucas numbers.

## Output

Returns a JSON object containing the n-th term, partial sum, infinite sum (for convergent geometric series), average, first term, and common difference/ratio. May also include a summary string, degraded flag, and disclaimer notes.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "type",
      "n"
     ],
     "properties": {
      "n": {
       "type": "integer",
       "description": "Number of terms, or the index for fibonacci and lucas (up to 5000)"
      },
      "step": {
       "type": "number",
       "description": "Common difference (arithmetic) or common ratio (geometric)"
      },
      "type": {
       "type": "string",
       "description": "arithmetic, geometric, fibonacci or lucas"
      },
      "first": {
       "type": "number",
       "description": "First term (arithmetic, geometric)"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "n": {
       "type": [
        "null",
        "number"
       ]
      },
      "sum": {
       "type": [
        "null",
        "number"
       ]
      },
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "average": {
       "type": [
        "null",
        "number"
       ]
      },
      "nthTerm": {
       "type": [
        "null",
        "number"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "firstTerm": {
       "type": [
        "null",
        "number"
       ]
      },
      "disclaimer": {
       "type": [
        "null",
        "string"
       ]
      },
      "notChecked": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "commonDifference": {
      
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/sequence-sum-solver-arithmetic-geometric-fibonacci-lucas-3a29a149/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from math-geometry.x402tookit.com](https://www.zero.xyz/host/math-geometry.x402tookit.com/llms.txt)