Find the missing number: 2, 6, 12, 20, 30, ?, 56
Pattern: n(n+1) where n = 1,2,3,4,5,6,7. For n=6: 6×7 = 42
Complete the series: 1, 2, 3, 5, 8, 13, 21, ?, 55
Modified Fibonacci: 13 + 21 = 34
Find missing: 1, 3, 9, 27, 81, ?
Powers of 3: 3⁰, 3¹, 3², 3³, 3⁴, 3⁵. Missing is 3⁵ = 243
Find next term: 2, 3, 5, 7, 11, 13, ?, 19
Prime numbers sequence: 2, 3, 5, 7, 11, 13, 17, 19
Complete: 100, 50, 25, 12.5, ?, 3.125
Each term is divided by 2. 12.5 ÷ 2 = 6.25
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Find next: 1, 8, 27, 64, 125, ?
Perfect cubes: 1³, 2³, 3³, 4³, 5³, 6³. Missing is 6³ = 216
Complete the series: 3, 7, 16, 35, 74, ?
Each term = 2 × (previous term) + 1. So 2 × 74 + 7 = 155
Find the next term: 1, 3, 7, 15, 31, 63, ?
Each term = 2^n - 1. For n=7: 2^7 - 1 = 127
Complete: 4, 6, 12, 14, 28, 30, ?
Alternating operations: +2, ×2, +2, ×2, +2, ×2. So 30 × 2 = 60
Complete: 7, 14, 28, 35, 70, 77, ?
Pattern alternates: ×2, ×2, +7, ×2, +7, ×2. So 77 × 2 = 154
Find missing term: 2, 6, 12, 20, 30, 42, ?
Pattern: n(n+1) for n = 1, 2, 3... gives 2, 6, 12, 20, 30, 42, 56
Find next: 3, 12, 27, 48, 75, ?
Pattern: 3×1², 3×2², 3×3², 3×4², 3×5², 3×6² = 108
Complete: 1, 2, 4, 7, 11, 16, 22, ?
Differences form sequence 1, 2, 3, 4, 5, 6, 7: 22 + 7 = 29
Complete the series: 6, 13, 22, 33, 46, ?
Differences: 7, 9, 11, 13, 15. Pattern increases by 2 each time: 46 + 15 = 61
Find missing term: 10, 11, 13, 16, 20, 25, ?
Differences: 1, 2, 3, 4, 5, 6. So 25 + 6 = 31
Find next term: 100, 99, 97, 94, 90, ?
Differences are: -1, -2, -3, -4, -5. So next is 90 - 5 = 85
Complete: 1, 4, 16, 64, 256, ?
Each term is multiplied by 4 (powers of 4). 256 × 4 = 1024
Find next: 2, 5, 10, 17, 26, ?
Differences: +3, +5, +7, +9, +11. Next difference is +11, so 26 + 11 = 37
Complete the series: 1, 3, 6, 10, 15, 21, ?
Triangular numbers: 1, 1+2=3, 1+2+3=6, 1+2+3+4=10, etc. Next is 1+2+3+4+5+6+7 = 28
Complete: 5, 6, 8, 11, 15, 20, ?
Differences: +1, +2, +3, +4, +5, +6. So 20 + 6 = 26
