Sequence patternSHL Verify G+Cubiks Logiks Advanced
Multiply Then Add
Each term equals the previous term multiplied by a fixed number, then shifted by a constant.
The Multiply Then Add — sometimes called a linear recurrence sequence — combines multiplication and addition into one rule: next = previous × a + b. Differences between terms are not constant (so it is not arithmetic), and ratios are not constant (so it is not pure geometric). This combination is a deliberate trap in SHL Verify G+ assessments. Once you know what to look for, solving it takes about 20 seconds.
How to solve it
- 1Compute the differences — they are not constant. Compute the ratios — they are not constant either.
- 2Try the multiplier ×2: compute current − (previous × 2) for each pair. If this value is always the same, the rule is 'multiply by 2, then add [constant]'.
- 3If ×2 does not work, try ×3. The multiplier is almost always 2 or 3 in assessment questions.
- 4Once you have the rule (next = prev × a + b), apply it to the last term to find the answer.
- 5Alternatively: if the differences grow by a fixed ratio, the underlying rule is of this form.
Worked examples
Example 1
×2 + 1
2
5
11
23
47
?
Rule: next = previous × 2 + 1
2 → 52 × 2 + 1 = 5 ✓
5 → 115 × 2 + 1 = 11 ✓
11 → 2311 × 2 + 1 = 23 ✓
23 → 4723 × 2 + 1 = 47 ✓
47 → ?47 × 2 + 1 = 95
Answer: 95— 47 × 2 + 1 = 95
Example 2
×3 + 1
1
4
13
40
121
?
Rule: next = previous × 3 + 1
1 → 41 × 3 + 1 = 4 ✓
4 → 134 × 3 + 1 = 13 ✓
13 → 4013 × 3 + 1 = 40 ✓
40 → 12140 × 3 + 1 = 121 ✓
121 → ?121 × 3 + 1 = 364
Answer: 364— 121 × 3 + 1 = 364
Example 3
×2 − 3
6
9
15
27
51
?
Rule: next = previous × 2 − 3
6 → 96 × 2 − 3 = 9 ✓
9 → 159 × 2 − 3 = 15 ✓
15 → 2715 × 2 − 3 = 27 ✓
27 → 5127 × 2 − 3 = 51 ✓
51 → ?51 × 2 − 3 = 99
Answer: 99— 51 × 2 − 3 = 99
Common mistakes
- Only trying purely arithmetic (constant differences) or purely geometric (constant ratio). The hybrid requires testing both together.
- Testing too many multipliers. Start with ×2. If that fails, try ×3. These two cover the vast majority of assessment questions.
- Arithmetic errors when verifying the rule. Double-check by applying it to two or three term pairs before using it to answer.
Ready to practice?
Work through timed Multiply Then Add questions and track your accuracy.