Number Sequence Puzzles

In each set, the third number is the difference between the second and first: 10-6=4, 12-8=4, 13-7=6. For the last set, 13-5=8.

The sequence shows consecutive prime numbers starting from 7: 7, 13, 17, 19, 23. The next prime number after 23 is 29. 26 is not prime (2 × 13), 31 is the next prime after 29, and 37 is the next prime after 31.

The pattern alternates between halving and doubling with increasing factors: 60 ÷ 1 = 60, 60 × 2 = 120, 120 ÷ 4 = 30, 30 × 8 = 240. The next step is 240 ÷ 16 = 15. The division factors double each time (1, 2, 4, 8, 16) as do the multiplication factors.

Starting from 3, each term doubles the previous: 3, 6 (3×2), 12 (6×2), 24 (12×2), 48 (24×2). The next term is 48 × 2 = 96. 64 would be 2⁶, 78 doesn't follow the pattern, and 90 is unrelated to the doubling sequence.

The pattern alternates between adding 2 and doubling the previous result: 1 + 2 = 3, 3 × 2 = 6, 6 + 2 = 8, 8 × 2 = 16, 16 + 2 = 18, 18 × 2 = 36, 36 + 2 = 38, 38 × 2 = 76. The next step is 76 + 2 = 78.

The series follows a repeating pattern of +1, +2, +3. Starting from 5: 5+1=6, 6+2=8, 8+3=11, 11+1=12, 12+2=14, 14+3=17, 17+1=18, 18+2=20, 20+3=23. The next step is +1, giving 23+1=24.

In each triplet, the third number is the sum of the first two. 4+3=7, 5+6=11, 16+5=21. Therefore 12+4=16.

The series is cubes of consecutive natural numbers: 1³=1, 2³=8, 3³=27, 4³=64. The next term is 5³=125.

The series consists of triplets where adjacent numbers multiply to give the third: 5×4=20, 7×2=14, 3×6=18. The pattern is (first number) × (second number) = (third number).

The differences between consecutive terms are: 7-5=2, 10-7=3, 14-10=4. The differences increase by 1 each time (2, 3, 4). The next difference should be 5, so 14+5=19.

This is the Fibonacci sequence where each number (starting from the third) is the sum of the two preceding numbers. 21 + 34 = 55, making 55 the next number in the sequence. This pattern continues consistently throughout the series.

The differences between consecutive terms are 1, 8, 27, 64 - which are cubes: 1³, 2³, 3³, 4³. The next difference should be 5³ = 125. Therefore, 101 + 125 = 226 is the next number in the sequence.

The sequence follows n³ - 1: 2³-1=7, 3³-1=26, 4³-1=63, 5³-1=124. The next is 6³-1 = 216 - 1 = 215.

The pattern is (Term - 1) * 4 + 1 starting from the second term, or more simply: 4^0+1, 4^1+1, 4^2+1, 4^3+1. The next is 4^4+1 = 256 + 1 = 257.

The sequence follows the rule n² + n (or n(n+1)): 12, 23, 34, 45, 56, 67, 78. The next is 89 = 72.

The pattern is (Term * -4) + 1. (205 * -4) + 1 = -820 + 1 = -819.

This is a sequence of triangular numbers where the difference increases by 1 each time: +2, +3, +4, +5, +6, +7. The next difference is +8, so 28 + 8 = 36.

The sequence consists of squares of descending odd numbers: 19²(361), 17²(289), 15²(225), 13²(169), 11²(121). The missing value is 225.