Number Sequence Calculator
Arithmetic and geometric sequences (nth term, sum, first terms) and Fibonacci numbers.
Change the values and press Calculate to work out your own figures.
Arithmetic sequence
Enter the first term, the common difference and n.
Show the working
- aₙ = a₁ + (n − 1)d = 1 + 4 × 2 = 9
- Sₙ = n(a₁ + aₙ) ÷ 2 = 25
Geometric sequence
Enter the first term, the common ratio and n.
Show the working
- aₙ = a₁ × r^(n − 1) = 1 × 2^7 = 128
- Sₙ = a₁(1 − rⁿ) ÷ (1 − r) = 255
Fibonacci number
Enter n; F(0) = 0 and F(1) = 1.
Show the working
- F(0) = 0, F(1) = 1, F(n) = F(n − 1) + F(n − 2)
How to use it
Enter the first term, the common difference and n. Enter the first term, the common ratio and n. Enter n; F(0) = 0 and F(1) = 1.
Number boxes accept whole numbers, decimals, fractions (3/4), powers (2^10), roots (sqrt(2)) and the constants pi and e. Show the working lists the steps.
Key facts
aₙ = a₁ + (n − 1)d; aₙ = a₁rⁿ⁻¹; F(n) = F(n − 1) + F(n − 2)
Sums
Arithmetic: n(a₁ + aₙ) ÷ 2. Geometric: a₁(1 − rⁿ) ÷ (1 − r).
Questions
What is the 5th odd number?
9.
What is the sum of 1 + 2 + 4 + … + 128?
255.
Formulas
aₙ = a₁ + (n − 1)d; aₙ = a₁rⁿ⁻¹; F(n) = F(n − 1) + F(n − 2)
Sources
Limitations
- Expressions up to 500 characters; matrices up to 10 × 10.
- Big-number results up to 100,000 digits; factorials up to 10,000!.
- Numbers in words up to 10^102 (short scale).