What is the next number in the sequence: 2, 3, 5, 8, 12, 17?

What is the next number in the sequence: 2, 3, 5, 8, 12, 17?

• A. 20
• B. 22
• C. 23
• D. 30

Answer: (C)

To determine the next number in the sequence 2, 3, 5, 8, 12, 17, we can start by observing the differences between consecutive numbers: - The difference between 2 and 3 is 1. - The difference between 3 and 5 is 2. - The difference between 5 and 8 is 3. - The difference between 8 and 12 is 4. - The difference between 12 and 17 is 5. The differences we have noted form the sequence: 1, 2, 3, 4, 5. This suggests that the differences are increasing by 1 each time. Following this pattern, the next difference should be 6. Adding this difference of 6 to the last number in the original sequence (17) gives us: 17 + 6 = 23. Therefore, the next number in the sequence is 23, which corresponds to the choice provided. The pattern established by the difference of increasing integers (1, 2, 3, 4, 5,...) leads us directly to the conclusion.

To determine the next number in the sequence 2, 3, 5, 8, 12, 17, we can start by observing the differences between consecutive numbers:

• The difference between 2 and 3 is 1.

• The difference between 3 and 5 is 2.

• The difference between 5 and 8 is 3.

• The difference between 8 and 12 is 4.

• The difference between 12 and 17 is 5.

The differences we have noted form the sequence: 1, 2, 3, 4, 5. This suggests that the differences are increasing by 1 each time. Following this pattern, the next difference should be 6.

Adding this difference of 6 to the last number in the original sequence (17) gives us:

17 + 6 = 23.

Therefore, the next number in the sequence is 23, which corresponds to the choice provided. The pattern established by the difference of increasing integers (1, 2, 3, 4, 5,...) leads us directly to the conclusion.