Govt. Exams
Entrance Exams
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.
Pattern: Each term is 2 times the previous term plus 1. 3→2(3)+(-1)=5, 5→2(5)-1=9, 9→2(9)-1=17, 17→2(17)-1=33, 33→2(33)-1=65, 65→2(65)-1=129.
These are triangular numbers. Each term adds consecutive integers: 1, 1+2=3, 3+3=6, 6+4=10, 10+5=15, 15+6=21, 21+7=28, 28+8=36.
Pattern: n(n+1) where n starts from 1. 1×2=2, 2×3=6, 3×4=12, 4×5=20, 5×6=30, 6×7=42, 7×8=56.
Pattern: Each term is obtained by doubling the previous term and subtracting a decreasing value. 5→7 (+2), 7→11 (+4), 11→19 (+8), 19→35 (+16), 35→67 (+32). The differences are powers of 2.
Differences: +1, +2, +3, +4, +5, +6, +7. Next difference is 7, so 30 + 7 = 37
Differences: +1, +3, +5, +7, +9, +11. Next difference is 11, so 29 + 11 = 40
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
Factorial series: 1!, 2!, 3!, 4!, 5!, 6! = 720
Prime numbers series: 2, 3, 5, 7, 11, 13, 17, 19, 23
