Sequence Machine Game
Complete arithmetic and geometric number patterns using differences or ratios.
Choose Practice or Daily to begin.
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Instructions, device progress and accessibility
Choose Easy, Normal or Hard and select Practice or a daily puzzle based on the UTC date. Enter answers or choose a correction, then select Check answer. Hints and Undo mark a round as assisted. Best scores and progress are stored only in this browser; no account is needed.
Local progress is checked when play begins.
How to play Sequence Machine
Inspect the first four numbers. Decide whether the pattern adds a fixed number or multiplies by a fixed factor. Enter the fifth and sixth terms to finish the sequence.
Worked example
Example: 3, 6, 12, 24 is a geometric sequence with common ratio 2. The next two values are 48 and 96. In 5, 8, 11, 14, the common difference is 3.
Math formulas and key skills
Arithmetic: aₙ = a₁ + (n − 1)d. Geometric: aₙ = a₁ × r⁽ⁿ⁻¹⁾. The game includes negative differences and negative common ratios at higher difficulty.
Avoid common mistakes
Avoid assuming every sequence is additive. Test the ratios when differences vary; for alternating signs, the common ratio may be negative.
Frequently asked questions
What is the difference between arithmetic and geometric sequences?
Arithmetic sequences add a constant difference, while geometric sequences multiply by a constant ratio.
Does a sequence have to increase?
No. Sequences can decrease or alternate between positive and negative terms.