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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.
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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.