Arithmetic Sequence Calculator

Calculate the nth term, first terms, and finite sum of an arithmetic sequence

Example Results

1 examples

Check homework sequence values

Find the 8th term and the first 8 terms for an arithmetic sequence that starts at 3 and increases by 4.

{
  "result": {
    "nthTerm": 31,
    "sumOfTerms": 136
  }
}
View input parameters
{ "firstTerm": 3, "commonDifference": 4, "termIndex": 8, "numberOfTerms": 8 }

Key Facts

Category
Math, Date & Finance
Input Types
number
Output Type
json
Sample Coverage
4
API Ready
Yes

Overview

The Arithmetic Sequence Calculator is a straightforward mathematical utility designed to find the nth term and the finite sum of an arithmetic progression. By inputting the starting value and the constant difference between numbers, users can instantly generate specific sequence values and calculate the total sum of a defined number of terms without manual formula computation.

When to Use

  • •When you need to quickly find a specific term (nth term) in a linear number sequence.
  • •When calculating the total sum of a finite arithmetic progression for math assignments or financial modeling.
  • •When verifying manual calculations of common differences and sequence sums to prevent arithmetic errors.

How It Works

  • •Enter the starting number of your sequence in the 'First Term' field.
  • •Input the constant value added to each step in the 'Common Difference' field.
  • •Specify the 'Term Index (n)' to find a specific term, and the 'Number Of Terms' to calculate the total sum.
  • •The tool instantly calculates and returns the nth term and the sum of the sequence in a structured JSON format.

Use Cases

Solving high school or college algebra homework involving arithmetic progressions and series.
Calculating simple interest or linear depreciation over a specific number of financial periods.
Determining seating capacities in stadiums or auditoriums where each row increases by a fixed number of seats.

Examples

1. Checking Algebra Homework

Student
Background
A student is working on an algebra assignment and needs to find the 8th term and the sum of the first 8 terms of a sequence.
Problem
Manually calculating the sequence 3, 7, 11, 15... is time-consuming and prone to arithmetic errors.
How to Use
Set the First Term to 3, Common Difference to 4, Term Index to 8, and Number Of Terms to 8.
Example Config
{"firstTerm": 3, "commonDifference": 4, "termIndex": 8, "numberOfTerms": 8}
Outcome
The tool instantly outputs the 8th term as 31 and the sum of the first 8 terms as 136.

2. Calculating Auditorium Seating

Event Planner
Background
An event planner is organizing a venue where the first row has 20 seats, and each subsequent row adds 5 seats.
Problem
Need to quickly know how many seats are in the 15th row and the total capacity of the first 15 rows.
How to Use
Input 20 as the First Term, 5 as the Common Difference, and 15 for both the Term Index and Number Of Terms.
Example Config
{"firstTerm": 20, "commonDifference": 5, "termIndex": 15, "numberOfTerms": 15}
Outcome
The tool calculates that the 15th row has 90 seats, and the total capacity for 15 rows is 825 seats.

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FAQ

What is an arithmetic sequence?

An arithmetic sequence is an ordered list of numbers where the difference between any two consecutive terms is always constant.

What is the common difference?

The common difference is the fixed number added to each term to get the next term in the sequence. It can be positive, negative, or zero.

Can I use negative numbers for the inputs?

Yes, both the first term and the common difference accept negative numbers, allowing you to calculate decreasing sequences.

What is the maximum term index I can calculate?

You can calculate up to the 100,000th term index using this tool.

How is the sum of terms calculated?

The tool uses the standard arithmetic series formula to compute the sum based on your provided first term, common difference, and number of terms.

API Documentation

Request Endpoint

POST /en/api/tools/arithmetic-sequence-calculator

Request Parameters

Parameter Name Type Required Description
firstTerm number No -
commonDifference number No -
termIndex number No -
numberOfTerms number No -

Response Format

{
  "key": {...},
  "metadata": {
    "key": "value"
  },
  "error": "Error message (optional)",
  "message": "Notification message (optional)"
}
JSON Data: JSON Data

AI MCP Documentation

Add this tool to your MCP server configuration: 

{
  "mcpServers": {
    "elysiatools-arithmetic-sequence-calculator": {
      "name": "arithmetic-sequence-calculator",
      "description": "Calculate the nth term, first terms, and finite sum of an arithmetic sequence",
      "baseUrl": "https://elysiatools.com/mcp/sse?toolId=arithmetic-sequence-calculator",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

You can chain multiple tools, e.g.: `https://elysiatools.com/mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp`, max 20 tools.

If you encounter any issues, please contact us at [email protected]