3, 6, 12, 24, 48, ?, 192
Each term is multiplied by 2. 48×2 = 96
2, 5, 10, 17, 26, ?, 50
Pattern: n² + 1 where n = 1,2,3,4,5,6. So 6² + 1 = 37
Complete: 1, 2, 4, 7, 11, 16, ?
Differences increase by 1: +1, +2, +3, +4, +5, +6. So 16+6 = 22
Find next: 5, 6, 8, 11, 15, ?
Differences: +1, +2, +3, +4, +5. So 15+5 = 20
3, 9, 27, 81, ?, 729
Powers of 3: 3¹, 3², 3³, 3⁴, 3⁵, 3⁶. Missing is 3⁵ = 243
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2, 6, 18, 54, ?, 486
Each term multiplied by 3. 54×3 = 162
1, 3, 6, 10, 15, 21, ?, 36
Triangular numbers: 1, 1+2, 1+2+3, etc. Missing is 1+2+3+4+5+6+7 = 28
144, 72, 36, 18, ?, 4.5
Each term divided by 2. 218 = 9
Complete the series: 5, 11, 23, 47, 95, ?
Pattern: Multiply by 2 and add 1. (95 × 2) + 1 = 191
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
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
