Arithmetic and geometric sequence calculator
Find the general term, the nth term and the sum of the terms of arithmetic and geometric sequences, with the list of terms and the sum of an infinite geometric series.
How to useArithmetic and geometric sequences
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Arithmetic and geometric sequence calculator: what it is for
Choose an arithmetic or geometric sequence and enter the first term, the common difference or ratio and the number of terms. The calculator shows the general term, the value of the nth term, the sum of the terms, the sum of the infinite geometric series when it exists, and lists the terms of the sequence.
How to use
- Choose arithmetic or geometric.
- Enter the first term, the difference or ratio, and n.
- See the term, the sum and the list.
When to use it
- Studying for math tests and exams.
- Checking sequence exercises.
- Simulating linear and exponential growth.
Frequently asked questions
What is the formula for the nth term of an arithmetic sequence?
aₙ = a₁ + (n − 1) × d, where d is the common difference. The sum of the first n terms is Sₙ = (a₁ + aₙ) × n ÷ 2.
And for a geometric sequence?
aₙ = a₁ × rⁿ⁻¹, where r is the common ratio. The sum of the first n terms is Sₙ = a₁ × (rⁿ − 1) ÷ (r − 1), for r other than 1.
When does an infinite geometric series have a sum?
When the ratio is between −1 and 1. In that case the sum converges to a₁ ÷ (1 − r).
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