- Find the missing number in this sequence: 3,7,15,31,?
Answer: 63
The pattern is that each term is double the previous term plus 1: 3 × 2 + 1 = 7, 7 × 2 + 1 = 15, 15 × 2 + 1 = 31, so 31 × 2 + 1 = 63. Choice A (47) represents adding 16 to 31. Choice B (55) represents adding 24 to 31. Choice D (67) represents doubling 31 and adding 5.
- In the sequence 2,5,11,23,47,?, what is the next term?
Answer: 95
Each term is double the previous term plus 1: 2 × 2 + 1 = 5, 5 × 2 + 1 = 11, 11 × 2 + 1 = 23, 23 × 2 + 1 = 47, so 47 × 2 + 1 = 95. Choice A (71) adds 24 to 47. Choice B (85) represents doubling 47 and subtracting 9. Choice D (99) represents doubling 47 and adding 5.
- What is the missing number in this pattern: 4,11,25,53,?
Answer: 109
Each term follows the pattern of doubling the previous term and adding 3: 4 × 2 + 3 = 11, 11 × 2 + 3 = 25, 25 × 2 + 3 = 53, so 53 × 2 + 3 = 109. Choice A (105) represents doubling 53 and subtracting 1. Choice B (107) represents doubling 53 and adding 1. Choice D (111) represents doubling 53 and adding 5.
- In the sequence 2,6,18,54,?, what number comes next?
Answer: 162
This is a geometric sequence where each term is multiplied by 3. The pattern is: 2 × 3 = 6, 6 × 3 = 18, 18 × 3 = 54, so 54 × 3 = 162. Choice A (108) represents doubling the last term. Choice C (144) comes from adding 90 to 54. Choice D (216) represents multiplying by 4 instead of 3.
- What number continues this series: 1,8,27,64,?
Answer: 125
This sequence represents perfect cubes: 1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, so 5³ = 125. Choice A (100) represents 10². Choice C (128) represents 2⁷ or doubling 64. Choice D (216) represents 6³, skipping one number in the pattern.
- What is the next number in the series: 1,4,9,16,25,?
Answer: 36
This sequence represents perfect squares: 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, so 6² = 36. Choice A (30) represents adding 5 to the last term. Choice B (35) represents adding 10 to the last term. Choice D (49) represents 7², skipping one number in the pattern.
- Find the next number: 5,12,26,54,?
Answer: 110
The pattern is that each term is double the previous term plus 2: 5 × 2 + 2 = 12, 12 × 2 + 2 = 26, 26 × 2 + 2 = 54, so 54 × 2 + 2 = 110. Choice A (108) represents doubling 54. Choice C (112) represents doubling 54 plus 4. Choice D (118) represents doubling 54 plus 10.
- Complete this number sequence: 7,21,63,189,?
Answer: 567
This is a geometric sequence where each term is multiplied by 3: 7 × 3 = 21, 21 × 3 = 63, 63 × 3 = 189, so 189 × 3 = 567. Choice A (378) represents doubling 189. Choice B (441) represents adding 252 to 189. Choice C (504) represents adding 315 to 189.
- What number should come next in the pattern: 100,91,83,76,?
Answer: 70
The differences between consecutive terms are decreasing by 1 each time: 100 - 91 = 9, 91 - 83 = 8, 83 - 76 = 7, so the next difference should be 6, making 76 - 6 = 70. Choice A (68) subtracts 8 again. Choice B (69) subtracts 7 again. Choice D (71) subtracts 5.
- In the series 81,72,64,57,51,?, what comes next?
Answer: 46
The differences between consecutive terms are increasing by 1 each time: 81 - 72 = 9, 72 - 64 = 8, 64 - 57 = 7, 57 - 51 = 6, so the next difference should be 5, making 51 - 5 = 46. Choice A (44) subtracts 7 again. Choice B (45) subtracts 6 again. Choice D (47) subtracts 4.
- Based on the bar graph shown, which number should come next in the sequence?
Answer: 64
The bar heights are 4, 8, 16, 32—each bar doubles. The next height doubles again: 32 × 2 = 64. Other options are larger multiples that do not follow pure doubling.
