数列計算ツール
The detailed guide below is currently available in English.
The three sequence families
An arithmetic sequence adds the same difference every step: 1, 3, 5, 7 has difference 2, and its first n terms sum to n × (first + last) ÷ 2. A geometric sequence multiplies by the same ratio — 1, 2, 4, 8 doubles each time — and its sum follows n·terms via a × (rⁿ − 1) ÷ (r − 1) when r ≠ 1, growing explosively for ratios above 1. Fibonacci-style sequences add the two previous terms, a rule that appears in growth patterns from rabbit populations to spiral shells. This calculator lists every term so the pattern is visible, with the total sum as the headline.
よくある質問
What happens with a negative common difference or ratio?
Negative differences make arithmetic sequences count downward (10, 7, 4…), and negative ratios make geometric sequences alternate sign (2, −6, 18…). Both are valid and sum normally.
Can the Fibonacci tab start with numbers other than 1, 1?
Yes — any two starting terms work, such as 2, 5 giving 2, 5, 7, 12, 19. The rule "each term is the sum of the previous two" stays the same regardless of the seeds.