(1) 2, 5, 10, 17, 26, ?
(2) 3, 6, 12, 24, 48, ?
(3) 5, 11, 17, 23, 29, ?
(4) 1, 4, 9, 16, 25, ?
(5) 7, 14, 28, 56, 112, ?
(6) 2, 3, 5, 8, 12, ?
(7) 1, 1, 2, 6, 24, ?
(8) 3, 9, 27, 81, ?
(9) 10, 15, 20, 25, 30, ?
(10) 8, 16, 32, 64, 128, ?
(11) 2, 4, 8, 16, 32, ?
(12) 1, 3, 9, 27, 81, ?
(13) 100, 90, 80, 70, 60, ?
(14) 2, 5, 11, 20, 32, ?
(15) 0, 1, 1, 2, 3, 5, ?
(16) 12, 24, 48, 96, 192, ?
(17) 5, 11, 21, 35, 53, ?
(18) 1, 4, 7, 10, 13, ?
(19) 3, 7, 13, 21, 31, ?
(20) 6, 13, 19, 27, 36, ?
(21) 10, 12, 14, 16, 18, ?
(22) 5, 12, 21, 32, 45, ?
(23) 4, 9, 19, 39, 79, ?
(24) 1, 3, 9, 27, 81, ?
(25) 7, 14, 28, 56, 112, ?
Answers
(1) 2, 5, 10, 17, 26, ?
Answer: 37
Explanation: The difference between consecutive numbers increases by 1 (3, 5, 7, 9, …). So, the next difference is 11:
26 + 11 = 37.
(2) 3, 6, 12, 24, 48, ?
Answer: 96
Explanation: Each number is multiplied by 2:
48 × 2 = 96.
(3) 5, 11, 17, 23, 29, ?
Answer: 35
Explanation: The difference between consecutive numbers is 6, 6, 6, 6, … So, the next number is:
29 + 6 = 35.
(4) 1, 4, 9, 16, 25, ?
Answer: 36
Explanation: These are perfect squares: 12,22,32,42,52,…. The next perfect square is 62=36.
(5) 7, 14, 28, 56, 112, ?
Answer: 224
Explanation: Each number is multiplied by 2:
112 × 2 = 224.
(6) 2, 3, 5, 8, 12, ?
Answer: 17
Explanation: The difference between consecutive numbers increases by 1 (1, 2, 3, 4, …). So, the next difference is 5:
12 + 5 = 17.
(7) 1, 1, 2, 6, 24, ?
Answer: 120
Explanation: Each number is the factorial of the position in the series:
1!=1, 2!=2, 3!=6, 4!=24, 5!=120.
(8) 3, 9, 27, 81, ?
Answer: 243
Explanation: Each number is multiplied by 3:
81 × 3 = 243.
(9) 10, 15, 20, 25, 30, ?
Answer: 35
Explanation: The difference between consecutive numbers is 5:
30 + 5 = 35.
(10) 8, 16, 32, 64, 128, ?
Answer: 256
Explanation: Each number is multiplied by 2:
128 × 2 = 256.
(11) 2, 4, 8, 16, 32, ?
Answer: 64
Explanation: Each number is multiplied by 2:
32 × 2 = 64.
(12) 1, 3, 9, 27, 81, ?
Answer: 243
Explanation: Each number is multiplied by 3:
81 × 3 = 243.
(13) 100, 90, 80, 70, 60, ?
Answer: 50
Explanation: The difference between consecutive numbers is -10:
60 – 10 = 50.
(14) 2, 5, 11, 20, 32, ?
Answer: 47
Explanation: The differences between consecutive numbers are increasing by 1 (3, 6, 9, 12, …):
32 + 15 = 47.
(15) 0, 1, 1, 2, 3, 5, ?
Answer: 8
Explanation: This is the Fibonacci sequence: each number is the sum of the two preceding ones:
5 + 3 = 8.
(16) 12, 24, 48, 96, 192, ?
Answer: 384
Explanation: Each number is multiplied by 2:
192 × 2 = 384.
(17) 5, 11, 21, 35, 53, ?
Answer: 75
Explanation: The differences between consecutive numbers are 6, 10, 14, 18, … (increasing by 4):
53 + 22 = 75.
(18) 1, 4, 7, 10, 13, ?
Answer: 16
Explanation: The difference between consecutive numbers is 3:
13 + 3 = 16.
(19) 3, 7, 13, 21, 31, ?
Answer: 43
Explanation: The difference between consecutive numbers is 4, 6, 8, 10, … (increasing by 2):
31 + 12 = 43.
(20) 6, 13, 19, 27, 36, ?
Answer: 46
Explanation: The difference between consecutive numbers is increasing by 2: 7, 8, 9, 10, … So, the next difference is 11:
36 + 11 = 46.
(21) 10, 12, 14, 16, 18, ?
Answer: 20
Explanation: The difference between consecutive numbers is 2:
18 + 2 = 20.
(22) 5, 12, 21, 32, 45, ?
Answer: 60
Explanation: The differences between consecutive numbers are 7, 9, 11, 13, … (increasing by 2):
45 + 15 = 60.
(23) 4, 9, 19, 39, 79, ?
Answer: 159
Explanation: The differences between consecutive numbers are 5, 10, 20, 40, … (increasing by 5, 10, 20, …):
79 + 80 = 159.
(24) 1, 3, 9, 27, 81, ?
Answer: 243
Explanation: Each number is multiplied by 3:
81 × 3 = 243.
(25) 7, 14, 28, 56, 112, ?
Answer: 224
Explanation: Each number is multiplied by 2:
112 × 2 = 224.