# Geometric Sequence Calculator Calculate the nth term, first terms, and finite sum of a geometric sequence > Canonical page: https://elysiatools.com/en/tools/geometric-sequence-calculator - **Category:** Math & Numbers - **Keywords:** geometric sequence, sequence, common ratio, nth term, sum of terms, math ## Overview The Geometric Sequence Calculator is a straightforward mathematical utility designed to find the nth term and the finite sum of a geometric progression. By entering the first term and the common ratio, you can instantly compute specific terms and the total sum of the sequence without manual calculations, making it an ideal tool for students, educators, and analysts modeling exponential growth or decay. ## Inputs - **First Term** (number) - **Common Ratio** (number) - **Term Index (n)** (number) - **Number Of Terms** (number) ## When to use - When you need to find a specific term (nth term) in a geometric progression without writing out the entire sequence manually. - When calculating the finite sum of a geometric series for mathematical assignments or financial modeling. - When verifying manual calculations of exponential growth, compound interest, or decay problems. ## How it works - Enter the starting value of your sequence in the 'First Term' field. - Input the multiplier between consecutive terms into the 'Common Ratio' field. - Specify the 'Term Index (n)' to find a specific value, and the 'Number Of Terms' to calculate the finite sum. - The calculator instantly processes the inputs and outputs the exact nth term and the sum of the specified terms. ## Use cases - Solving algebra and calculus homework problems involving geometric progressions and series. - Modeling compound interest, population growth, or asset depreciation over a fixed number of periods. - Generating test cases and answer keys for math educators teaching exponential patterns. ## Frequently asked questions ### What is a geometric sequence? A geometric sequence is a series of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. ### What is the common ratio? The common ratio is the constant factor between consecutive terms in a geometric sequence. For example, in the sequence 2, 6, 18, the common ratio is 3. ### Can the common ratio be a negative number or a fraction? Yes, the common ratio can be negative (which creates an alternating sequence) or a decimal/fraction (which creates a decaying or shrinking sequence). ### What is the maximum term index I can calculate? This calculator supports finding up to the 1000th term in a geometric sequence. ### How is the sum of terms calculated? The tool uses the standard geometric series sum formula, taking your first term, common ratio, and the specified number of terms (up to 50) to compute the exact finite sum. ## Related tools - [Active Earth Pressure (Rankine)](https://elysiatools.com/en/tools/active-earth-pressure): Calculate the Rankine active earth pressure on a smooth vertical wall backfilled with cohesionless soil. K_a = tan²(45°−φ/2). Optional uniform surcharge q. 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