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
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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
Find the missing term: 10, 11, 13, 16, 20, 25, 31, ?
Differences: +1, +2, +3, +4, +5, +6, +7. Next is 31 + 7 = 38
Complete: 2, 6, 18, 54, 162, ?
Each term is multiplied by 3. 162 × 3 = 486
Find next: 1, 2, 3, 5, 8, 13, 21, 34, ?
Fibonacci sequence: 34 + 21 = 55
Complete the series: 3, 9, 27, 81, 243, ?
Powers of 3: 3¹, 3², 3³, 3⁴, 3⁵, 3⁶ = 729
Find missing term: 4, 6, 9, 13, 18, 24, ?
Differences: +2, +3, +4, +5, +6, +7. So 24 + 7 = 31
Find missing term: 2, 5, 10, 17, 26, 37, ?
Differences: +3, +5, +7, +9, +11, +13. Next difference is 13, so 37 + 13 = 50
Complete the series: 6, 11, 21, 36, 56, ?
Differences: +5, +10, +15, +20, +25. Next difference is 25, so 56 + 25 = 81
Find next: 1, 3, 6, 10, 15, 21, ?, 36
Triangular numbers: 1, 1+2=3, 3+3=6, 6+4=10, 10+5=15, 15+6=21, 21+7=28
Complete: 4, 6, 9, 13, 18, 24, 31, ?
Differences: +2, +3, +4, +5, +6, +7, +8. Next difference is 8, so 31 + 8 = 39
Find next term: 1, 2, 4, 7, 11, 16, 22, ?
Differences: +1, +2, +3, +4, +5, +6, +7. Next difference is 7, so 22 + 7 = 29
Complete: 100, 99, 97, 94, 90, 85, ?, 70
Differences: -1, -2, -3, -4, -5, -6, -7, -8. After 85, subtract 6 to get 79
