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Lizely

Geometric Sequence Quiz

Practice five disclosed geometric sequences, including negative, zero, and unit ratios, and audit each missing term on the way to 1,000.

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How to use

  1. 1.Read the displayed first term and common ratio, then multiply repeatedly or use aₙ = a₁rⁿ⁻¹ to recover the highlighted missing position.
  2. 2.Type a signed number and press Enter or Check term. Blank and malformed input are ignored, while the same parsed wrong value cannot count twice.
  3. 3.Submit 24, -40, 0, -4, and 162 in order to solve all five fixed cards and finish with exactly 1,000 points.

About Geometric Sequence Quiz

Geometric Sequence Quiz is a focused browser exercise for the standard rule behind geometric sequences. Each card displays a first term, a common ratio, and five positions with one term hidden. The mathematical definition and formulas are cross-checked against OpenStax College Algebra 2e and an independently published Mathematics LibreTexts Advanced Algebra page. The particular cards, missing positions, two-error rule, and score are fixed Lizely game fixtures.

A geometric sequence repeatedly multiplies the preceding term by a constant common ratio. In recursive form, a term equals the previous term times r. In explicit form, a subscript-n term equals the first term times r raised to n minus one. The quiz displays both the first term and r on every card, so no factual rule is hidden and every answer can be recomputed from the page.

The first card starts at 3 with ratio 2 and hides the fourth term, 24. The second starts at 5 with ratio -2 and hides -40, making the sign alternate. The third starts at 7 with ratio 0 and hides 0 after the sequence has collapsed to zero. The fourth starts at -4 with ratio 1 and hides another -4. The fifth starts at 2 with ratio 3 and hides 162. These answers are independently written as literal test values rather than generated as their own expected results.

Every correct answer advances one fixed card and awards 200 points. Entering 24, -40, 0, -4, and 162 in order completes all five cards and produces exactly 1,000 points. An empty, whitespace-only, nonnumeric, exponential-notation, nonfinite, or malformed entry is an atomic no-op. It cannot advance the round, alter score, or spend an error.

A valid numeric value that is not the missing term creates one recoverable error. The stored signature uses the round and parsed numeric value, so equivalent repeats such as 999 and 999.0 are deduplicated. A second distinct numeric error anywhere in the run closes the quiz. Completion and deadlock freeze later submissions. Restart reconstructs the first card, clears the input and errors, and restores zero score.

Use the signed-number field and Check term button with a pointer or touch screen. Keyboard players can tab to the field, type a decimal or signed integer, and press Enter to submit. The responsive five-cell card, current card number, first term, common ratio, formula, audited score, error count, and feedback remain visible. R restarts when focus is not in an editing field, and the shared Boss Key remains available through the existing game shell.

The sequence generator accepts only finite first terms and ratios and an integer length from one through twenty. It normalizes negative zero for clear display and rejects nonfinite intermediate values rather than returning misleading output. The product quiz itself uses five modest integer fixtures, avoiding rounding ambiguity and allowing exact equality. No account, upload, API, model, network call, or new dependency is required.

Evidence includes eight literal formula-evaluation vectors: positive, negative, fractional, zero, and unit ratios, plus negative first terms. Independent tests compare those vectors with the production generator, restate all five quiz questions and answers, replay the exact 1,000-point route, prove the two-distinct-error route, deduplicate numerically equivalent wrong input, verify invalid input atomicity, and freeze both terminal states.

This practice game is educational entertainment, not a graded exam, placement test, tutoring guarantee, or aptitude assessment. A score measures completion of these five disclosed cards only. The citations support the mathematical definition and formula; they do not endorse the product's scoring, interface, or game rules.

Methodology & sources

Apply the cited geometric-sequence recurrence a_n=r a_(n-1) and explicit formula a_n=a_1 r^(n-1) to five fixed integer questions. Generate five terms with finite inputs and bounded length, require strict plain-decimal parsing, award 200 per literal correct missing term, and total exactly 1,000 after five cards. Treat blank, malformed, exponential, and nonfinite input atomically; deduplicate a round-and-numeric-value error signature; deadlock on the second distinct error; freeze terminal states. Cross-check the formula with OpenStax and LibreTexts, and independently restate at least eight literal evaluation vectors plus every quiz answer.

Frequently asked questions

What makes a sequence geometric?
Each term is the previous term multiplied by the same common ratio r. Equivalently, the nth term is a₁ times r raised to n minus one.
Does the quiz include negative or zero ratios?
Yes. The fixed cards include r=-2, r=0, and r=1 as well as positive ratios 2 and 3, so sign changes and constant sequences are explicit.
How are wrong answers counted?
The first distinct numeric error is recoverable. An equivalent repeat such as 999 and 999.0 is ignored, while a second distinct numeric error closes the run.

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