# Arithmetic Sequence Calculator Calculate the nth term, first terms, and finite sum of an arithmetic sequence > Canonical page: https://elysiatools.com/en/tools/arithmetic-sequence-calculator - **Category:** Math & Numbers - **Keywords:** arithmetic sequence, sequence, common difference, nth term, sum of terms, math ## 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. ## Inputs - **First Term** (number) - **Common Difference** (number) - **Term Index (n)** (number) - **Number Of Terms** (number) ## 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. ## Frequently asked questions ### 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. ## Related tools - [Antilog Calculator](https://elysiatools.com/en/tools/antilog-calculator): Calculate antilogarithms for any valid base and optionally verify the result by applying the logarithm again - [Bearing Capacity Calculator (Terzaghi)](https://elysiatools.com/en/tools/bearing-capacity-calculator): Calculate the Terzaghi ultimate bearing capacity of a shallow foundation: q_ult = c·Nc·sc + q·Nq·sq + 0.5·γ·B·Nγ·sγ. Computes Nc/Nq/Nγ and shape factors automatically; supports strip, square, and circular footings. Result in kPa. - [Belt Pulley Speed Ratio Calculator](https://elysiatools.com/en/tools/belt-pulley-speed-ratio): Calculate the ratio, driven speed and belt linear speed of a belt drive. i = d₂/d₁ = n₁/n₂, belt speed v = π·d·n/60. 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