Geometric sequence calculator
Published On: 04/03/2026
Geometric Sequence Calculator
Generate a geometric sequence and calculate the n-th term and the sum of the first n terms. A geometric sequence multiplies each term by a constant value called the common ratio.
Inputs explained:
• First term (a₁): the starting value in the sequence.
• Common ratio (r): the multiplier between consecutive terms (can be negative or fractional).
• Number of terms (n): how many terms to generate and sum.
• Rounding: controls how many decimals appear in results.
• First term (a₁): the starting value in the sequence.
• Common ratio (r): the multiplier between consecutive terms (can be negative or fractional).
• Number of terms (n): how many terms to generate and sum.
• Rounding: controls how many decimals appear in results.
Tip: If r = 1, the sequence is constant (same value each time). If |r| < 1, terms shrink toward 0.
Geometric Sequence Calculator — Description
The Geometric Sequence Calculator generates the terms of a geometric sequence and calculates both the n-th term and the sum of the first n terms. A geometric sequence is a list of numbers where each term is found by multiplying the previous term by a constant number called the common ratio.
Nth term: aₙ = a₁ × r^(n − 1)
Sum (r ≠ 1): Sₙ = a₁ × (1 − r^n) / (1 − r)
Sum (r = 1): Sₙ = a₁ × n
Enter the first term (a₁), the common ratio (r), and the number of terms (n). The calculator will output the full sequence, the n-th term, and the total sum—useful for algebra homework, SAT/ACT prep, and exponential growth/decay problems.