수학
Number Sequence Calculator
Calculate the nth term and the sum of arithmetic or geometric sequences.
사용 방법
- Select the type of sequence. Arithmetic means adding a constant number. Geometric means multiplying by a constant number.
- Enter the First Term of your sequence.
- Enter the Common Difference (for arithmetic) or Common Ratio (for geometric).
- Enter n (the number of terms you want to evaluate).
- The calculator will find the specific value of the nth term and the sum of all terms up to n.
공식
Arithmetic Sequence:
nth Term (aₙ) = a₁ + (n - 1)d
Sum (Sₙ) = (n/2) × (a₁ + aₙ)
Geometric Sequence:
nth Term (aₙ) = a₁ × r(n - 1)
Sum (Sₙ) = a₁ × (1 - rn) / (1 - r) (for r ≠ 1)
nth Term (aₙ) = a₁ + (n - 1)d
Sum (Sₙ) = (n/2) × (a₁ + aₙ)
Geometric Sequence:
nth Term (aₙ) = a₁ × r(n - 1)
Sum (Sₙ) = a₁ × (1 - rn) / (1 - r) (for r ≠ 1)
A Number Sequence Calculator is incredibly useful in discrete mathematics. Whether you are dealing with an arithmetic progression (like counting by 3s) or a geometric progression (like doubling your money every year), this tool provides the nth term, the sum of the series, and the explicit formula.