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1.  
1, 4, 12, 41, 170, ?

Correct Answer: C [857]

Explanation:

× 1 + 3, × 2 + 4, × 3 + 5, × 4 + 6, × 5 + 7: 170 × 5 + 7 = 857.

2.  
15, 29, 54, 99, 182, ?

Correct Answer: A [339]

Explanation:

× 2 − 1², × 2 − 2², …: 182 × 2 − 5² = 339.

3.  
Series I: 3, 7, 16, 35, 74. Series II follows the same rule: 5, a, b, c, d. Find c.

Correct Answer: B [51]

Explanation:

Rule × 2 + 1, × 2 + 2, × 2 + 3, × 2 + 4: a = 11, b = 24, c = 24 × 2 + 3 = 51.

4.  
Series I: 5, 6, 14, 45, 184. Series II follows the same rule: 3, a, b, c, d. Find b.

Correct Answer: D [10]

Explanation:

Rule × 1 + 1, × 2 + 2, × 3 + 3, × 4 + 4: a = 4, b = 4 × 2 + 2 = 10.

5.  
Find the wrong number: 4, 6, 16, 54, 222, 1130

Correct Answer: E [222]

Explanation:

Rule × n + 2n: 54 × 4 + 8 = 224, not 222.

6.  
Find the wrong number: 1, 2, 6, 15, 31, 56, 93

Correct Answer: D [93]

Explanation:

Differences 1², 2², …, 6²: 56 + 36 = 92, not 93.

7.  
Quantity I: the next term of 4, 18, 48, 100, 180
Quantity II: 300

Correct Answer: B [Quantity I < Quantity II]

Explanation:

n³ − n² (n = 2 to 6): 7³ − 7² = 343 − 49 = 294 < 300.

8.  
2, 10, ?, 68, 130, 222

Correct Answer: C [30]

Explanation:

n³ + n: 2, 10, 30, 68, 130, 222 (1³ + 1, 2³ + 2, 3³ + 3 …).

9.  
3, 11, 43, 171, 683, ?

Correct Answer: E [2,731]

Explanation:

× 4 − 1: 683 × 4 − 1 = 2,731.

10.  
2, 6, 10, 30, 34, 102, 106, ?

Correct Answer: A [318]

Explanation:

× 3 and + 4 take turns: 106 × 3 = 318.

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