Fast, Free & Accurate Online IQ Test

This question tests your ability to recognize and extend numerical patterns in a sequence. The given sequence is: 1, 1, 3, 6, 12, 22, 39, 67, 113, 188, ?

To find the next number in the series, we first analyze the differences between consecutive terms:

• 1 to 1: +0
• 1 to 3: +2
• 3 to 6: +3
• 6 to 12: +6
• 12 to 22: +10
• 22 to 39: +17
• 39 to 67: +28
• 67 to 113: +46
• 113 to 188: +75

Observing these differences: 0, 2, 3, 6, 10, 17, 28, 46, 75.

Next, analyze the pattern in these differences by finding the differences between them:

• 2 - 0 = 2
• 3 - 2 = 1
• 6 - 3 = 3
• 10 - 6 = 4
• 17 - 10 = 7
• 28 - 17 = 11
• 46 - 28 = 18
• 75 - 46 = 29

The second-level differences are: 2, 1, 3, 4, 7, 11, 18, 29.

Notice that each second-level difference is the sum of the two preceding second-level differences:

• 1 = 2 - 1
• 3 = 1 + 2
• 4 = 3 + 1
• 7 = 4 + 3
• 11 = 7 + 4
• 18 = 11 + 7
• 29 = 18 + 11

Following this pattern, the next second-level difference would be 18 + 29 = 47.

Therefore, the next first-level difference is 75 + 47 = 122.

Finally, adding this difference to the last term in the sequence: 188 + 122 = 310.

Thus, the correct answer is 310.