Track the multiplier, its sign and its exact value.
Review multiplication factors, negative ratios and exact decimal terms. These six answers concern a stated rule family, without a norm or certification.
The six questions each contribute one correct answer. The count describes this fixed rule family and edition, without a speed adjustment, IQ conversion or comparison with other people. Every worked answer and this complete guide is available at every count.
Multiplicative and additive models differ
These questions specify one constant multiplication factor between neighbouring terms. Look for a ratio rather than a fixed difference. A large-looking gap is not itself evidence of a particular factor: divide a later term by its predecessor and test the result across the row. The examples avoid division by zero, so those ratios are defined. This group measures neither financial growth forecasting nor a general ability; it checks six exact relationships under a supplied mathematical condition.
Verify a fresh growth factor
For 9, 36, 144, 576, ?, the ratios are all 4. Continuing gives 576 × 4 = 2304. The differences are 27, 108 and 432, so copying the last difference would not preserve the original relationship. Calculate a proposed next term only after checking the factor on the earlier transitions. When several alternatives are multiples of a displayed number, the size or familiarity of an option does not replace this consistency check.
Negative factors carry a sign rule
Consider 8, −24, 72, −216, ?. Multiplying by −3 changes the sign and triples the magnitude at each transition, giving 648 next. A factor of +3 would fit magnitude growth but fail the displayed signs. Conversely, alternating signs alone do not establish a factor: 8, −16, 48 has unequal ratios. Keep both magnitude and sign in the same equation, and test them together instead of treating the minus sign as decoration.
Shrinking rows still multiply
In 486, 162, 54, 18, ?, every step multiplies by one third, so the blank is 6. Saying “divide by three” describes the same operation. Shrinkage does not imply subtraction, and a factor between zero and one is perfectly valid. For a fresh exact-decimal example, 20, 15, 11.25, 8.4375 uses a factor of three quarters. Do not round intermediate terms unless a prompt explicitly requires rounding; this edition asks for exact values.
A missing middle term must reconnect the row
For 12, 18, ?, 40.5, 60.75, the ratio is 1.5, giving a blank of 27. Check both 18 × 1.5 = 27 and 27 × 1.5 = 40.5. Taking an arithmetic midpoint of 18 and 40.5 would use an additive model and produce the wrong value. Although a geometric mean can sometimes recover a missing term, direct multiplication keeps the stated factor and sign easier to inspect in these questions.
Explain which operation failed
For a wrong answer, divide each visible neighbouring pair, including negative signs, and compare the resulting ratios. If your factor is correct, inspect multiplication or target-position counting next. A calculator can check exact arithmetic but cannot decide which model the prompt requires. Build a new short sequence with a different starting value and your factor, then verify it backwards by division. This method is more informative than repeatedly clicking a known correct option in the fixed bank.
The family does not remove all mathematical alternatives
The answer key is checked against the constant-factor condition and the four displayed alternatives. Without that condition, a finite row can admit many other continuation formulas. Correctness here is therefore conditional on the stated model, not a universal proof of what must happen next in the world. The six-item count has no calibrated ability band, population percentile or certification value. All worked explanations remain available at zero, partial and perfect counts, and retakes may reflect memory after you have read them.