Arithmetic Sequence
aₙ = a₁ + (n − 1) × d
Where d = common difference
Geometric Sequence
aₙ = a₁ × r^(n−1)
Where r = common ratio
Custom Formula
aₙ = f(n)
Any formula in terms of n
The nth term of a sequence is a formula that allows you to find any term in the sequence without having to list all the preceding terms. It provides a direct relationship between the position (n) in the sequence and the value at that position. Understanding nth term formulas is fundamental in algebra, calculus, and many areas of mathematics and science.
For arithmetic sequences, each term differs from the previous by a constant amount called the common difference. For geometric sequences, each term is multiplied by a constant called the common ratio to get the next term. Custom formulas can represent more complex sequences like quadratic sequences, Fibonacci-related sequences, or any mathematical pattern.
- Select the sequence type: Choose Arithmetic, Geometric, or Custom formula.
- Enter the parameters: For arithmetic sequences, enter the first term and common difference. For geometric sequences, enter the first term and common ratio. For custom formulas, enter an expression in terms of n.
- Enter the term number: Specify which term (n) you want to find.
- Click Calculate: The calculator will compute the nth term and optionally show the step-by-step solution and sequence.
Nth term calculations follow standard mathematical formulas. Results depend on correct input values and selected sequence type. For custom formulas, ensure the expression is mathematically valid. Very large term numbers or ratios may result in numerical overflow.