2, 3, 5, 8, 13, 21, ?, 55
Modified Fibonacci: sum of previous two numbers. 13+21 = 34
1, 2, 6, 24, 120, ?, 5040
Factorial series: 1!, 2!, 3!, 4!, 5!, 6!, 7!. Missing is 6! = 720
1, 4, 13, 40, 121, ?, 1093
Pattern: 3ⁿ + 3ⁿ⁻¹ for n = 1,2,3,4,5,6. For n=6: 3⁶ + 3⁵ = 729 + 243 = 972... Review: Actually (3ⁿ - 1)/2. For n=6: (729-1)/2 = 364
2, 12, 36, 80, 150, ?, 448
Pattern: n(n² + 1) for n = 1,2,3,4,5,6,7. For n=6: 6(37) = 252
Find the missing number: 1, 4, 10, 20, 35, ?
Tetrahedral numbers or pattern with differences 3, 6, 10, 15, 19. Answer: 35 + 19 = 54
Advertisement
Complete: 3, 8, 15, 24, 35, ?, 63
Pattern: n² + 2n where n = 1,2,3,4,5,6,7. For n=6: 36 + 12 = 48
Complete the series: 2, 8, 18, 32, 50, ?, 98
Pattern: 2n² where n = 1,2,3,4,5,6,7. For n=6: 2(36) = 72
Find the next term: 2, 8, 18, 32, 50, 72, ?
Pattern: 2n(n+1) for n=1,2,3... gives 2, 8, 18, 32, 50, 72, 98
Complete the series: 5, 15, 30, 50, 75, ?
Pattern: 5×1, 5×3, 5×6, 5×10, 5×15, 5×21. Multipliers follow triangular numbers: 105
Complete: 7, 11, 16, 22, 29, 37, ?
Differences: +4, +5, +6, +7, +8, +9. So 37 + 9 = 46
Complete the series: 3, 7, 15, 31, 63, ?
Each term follows 2ⁿ - 1: (2¹-1), (2³-1), (2⁴-1), (2⁵-1), (2⁶-1), (2⁷-1) = 127
Complete: 1, 2, 6, 24, 120, ?
Factorial series: 1!, 2!, 3!, 4!, 5!, 6! = 720
Find missing term: 5, 11, 23, 47, 95, ?
Each term is (previous × 2) + 1: (5×2)+1=11, (11×2)+1=23, (23×2)+1=47, (47×2)+1=95, (95×2)+1=191
Complete the series: 4, 9, 25, 49, 121, 169, ?
Pattern: Squares of prime numbers. 2²=4, 3²=9, 5²=25, 7²=49, 11²=121, 13²=169, 17²=289. The series consists of squares of consecutive prime numbers.
