Geometric Sequence Calculator
Find the nth term and the sum of the first n terms of a geometric sequence.
Calculate
Enter your values below.
Result
nth term
0
Sum of first n terms
0
Formula used
aₙ = a₁ × r(n−1)
Sₙ = a₁(1 − rⁿ) ÷ (1 − r), for r ≠ 1
Example: First term 2, ratio 3, n=6 → 6th term = 486, sum = 728.
How to use this calculator
- Enter First term (a₁), Common ratio (r), Term number (n).
- Press Calculate to see your result instantly.
FAQ
Frequently asked questions
What is a geometric sequence?
A sequence where each term is found by multiplying the previous term by a fixed common ratio.
What if the ratio is 1?
Every term equals the first term, and the sum is simply a₁ × n.
Can the ratio be negative or a fraction?
Yes — a negative ratio alternates signs, and a fractional ratio shrinks the sequence toward zero.
Where are geometric sequences used?
Compound interest, population growth, and depreciation all follow geometric sequence patterns.