MATH CALCULATOR
Geometric Sequence Calculator
Calculate terms and sums of geometric sequences easily with our intuitive calculator.
What is the Geometric Sequence Calculator & How does it work?
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. For example, in the sequence 2, 6, 18, 54, …, the common ratio is 3.
The nth term of a geometric sequence can be calculated using the formula:
The sum of the first n terms of a geometric sequence can be calculated using the formula:
The nth term of a geometric sequence can be calculated using the formula:
a_n = a_1 times r^{(n-1)}
a_n = nth term
a_1 = first term
r = common ratio
n = term number
a_1 = first term
r = common ratio
n = term number
The sum of the first n terms of a geometric sequence can be calculated using the formula:
S_n = frac{a_1(1 – r^n)}{1 – r}
S_n = sum of first n terms
a_1 = first term
r = common ratio
n = number of terms
a_1 = first term
r = common ratio
n = number of terms
Parameters
Result—
Frequently Asked Questions
How do I find the common ratio in a geometric sequence?
Divide any term by its preceding term.
What is the formula for the nth term of a geometric sequence?
The nth term is calculated as a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.
Can you explain how to calculate the sum of the first n terms in a geometric sequence?
Yes, use the formula S_n = (a_1 * (1 - r^n)) / (1 - r), where a_1 is the first term, r is the common ratio, and n is the number of terms.
What if the common ratio is 1 in a geometric sequence?
If r = 1, the sequence is constant, and all terms are equal to the first term.
How do I use this calculator for a geometric sequence?
Input the first term, common ratio, and the term number or number of terms you want to calculate.
Can this calculator handle negative common ratios?
Yes, the calculator can handle both positive and negative common ratios.
What is a geometric sequence in math?
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.
Results are for informational purposes only and do not constitute professional advice.