Sequence Calculator
Arithmetic and geometric sequences — terms, sum, nth term
What is the Sequence Calculator?
A sequence calculator figures out the terms, sum, and nth term of arithmetic and geometric sequences. Arithmetic sequences increase by a fixed amount each step — like 3, 7, 11, 15. Geometric sequences multiply by a fixed ratio — like 2, 6, 18, 54. Both patterns come up in math class, financial modeling, and science. CalciHub's calculator handles both types: enter a few known values and it fills in the rest.
How Does It Work?
In an arithmetic sequence, you add the same number (common difference d) each time. In a geometric sequence, you multiply by the same number (common ratio r) each time. Finding the nth term lets you jump straight to any position without listing every term. The sum formula adds them all up without needing to write out the entire sequence.
Arithmetic: aₙ = a₁ + (n − 1)d, Sₙ = n/2 × (a₁ + aₙ) Geometric: aₙ = a₁ × rⁿ⁻¹, Sₙ = a₁ × (1 − rⁿ) / (1 − r) for r ≠ 1
• a₁ = first term of the sequence
• aₙ = nth term
• n = the position number you want
• d = common difference (arithmetic)
• r = common ratio (geometric)
• Sₙ = sum of the first n terms
How to Use CalciHub's Sequence Calculator
1. Choose the sequence type: arithmetic or geometric.
2. Enter the first term (a₁) and either the common difference (d) or common ratio (r).
3. Enter how many terms (n) you want.
4. Click Calculate — you'll see the term list, the nth term, and the sum.
Tip: If you only know two terms from the sequence (not the first), you can work out d or r first, then use this calculator for everything else.
A Quick Example
Arithmetic sequence: first term = 5, common difference = 4. Find the 10th term and the sum of the first 10 terms. The 10th term: a₁₀ = 5 + (10 − 1) × 4 = 5 + 36 = 41. Sum: S₁₀ = 10/2 × (5 + 41) = 5 × 46 = 230. The sequence runs 5, 9, 13, 17, 21, 25, 29, 33, 37, 41. Enter these values and CalciHub returns the same results in one step.
The sum formula is particularly powerful — instead of adding all 10 numbers manually, you just need the first and last terms and the count.
Frequently Asked Questions
Arithmetic sequences add a fixed amount at each step. Geometric sequences multiply by a fixed ratio. 2, 5, 8, and 11 are arithmetic (d = 3). 2, 6, 18, and 54 are geometric (r = 3).