Make a second row before choosing the next number.
Work through additive and multiplicative gap patterns, signed changes and middle blanks. Six local counts do not imply IQ, ranking or test readiness.
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.
The pattern may sit in the gaps
These questions restrict the gaps between consecutive terms to one of two families: the gaps add a fixed nonzero amount, or they multiply by a fixed factor. Write the gap row before deciding which condition fits. Do not apply a rule to the original terms simply because it works on the differences. This extra level is the subject of the six exercises. It is still a bounded practice model, not evidence that an unrestricted finite sequence has only one possible mathematical continuation.
A fresh second-difference calculation
For 5, 12, 23, 38, ?, the gaps are 7, 11 and 15. The gaps themselves add 4, so the next gap is 19 and the next original term is 38 + 19 = 57. Returning 19 would answer “what is the next gap?” rather than the actual question. Put a label above each row and show the final addition back into the original sequence. That simple bookkeeping step prevents a frequent level-of-description error.
Decreasing values can have increasing gaps
Consider 70, 58, 48, 40, 34, ?. Signed gaps are −12, −10, −8 and −6. Each increases by 2, so the next is −4 and the missing value is 30. A statement that the gaps increase refers to their signed values, not their absolute sizes. Writing unsigned distances 12, 10, 8, 6 can still help, but you must restore subtraction when returning to the original row. Mixing the two conventions halfway can reverse the continuation.
A multiplier can act on the differences
For 10, 13, 19, 31, 55, ?, the gaps are 3, 6, 12 and 24. Doubling gives the next gap 48, and 55 + 48 = 103. Multiplying 55 by two would give 110 and would use a rule that already failed on earlier original terms. Check which row carries the multiplier. If gap signs alternate, a negative factor may explain them, but every gap must follow it; alternating appearance alone is not a sufficient test.
Reconstruct both gaps around a blank
A blank inside a row hides two adjacent gaps. For 1, 6, ?, 28, 45, the required additive-gap pattern is 5, 9, 13, 17, yielding the missing term 15. Check 6 + 9 = 15 and 15 + 13 = 28. Looking only at the total jump from 6 to 28 loses the distinction between those two gaps. Candidate substitution is a useful alternative: insert each offered number and test the entire resulting gap row against the stated families.
Check a gap rule at more than one transition
One comparison between two gaps may suggest a rule but does not verify it. Test every available change in the gap row. If the increments are not constant and the ratios are not constant, the candidate does not meet this exercise’s stated alternatives. Do not introduce a new exception near the blank just to rescue a preferred answer. After reviewing an error, change a starting term while keeping the same gaps and recalculate; this helps separate the gap structure from memorized original values.
Changing gaps are not a forecast
These idealized rows are constructed examples, not measured time series. A rule that fits them should not be used to predict prices, demand, health outcomes or another person’s performance. The score is simply six checked choices under the specified gap models, with no time penalty or calibrated norm. Every explanation remains free. If arithmetic effort distracts from the structure, use paper or a calculator and record the assistance when comparing your own practice attempts. A later higher count may include learning the fixed keys.