When working with the sequence: 2, 3, 5, 8, 12, 17, what is the difference between consecutive terms?

When working with the sequence: 2, 3, 5, 8, 12, 17, what is the difference between consecutive terms?

• A. Increasing by 1
• B. Varied increases
• C. Constant increases
• D. No discernible pattern

Answer: (B)

To analyze the differences between the consecutive terms in the given sequence: 2, 3, 5, 8, 12, 17, we can start by calculating the differences: - The difference between the first term (2) and the second term (3) is 1. - The difference between the second term (3) and the third term (5) is 2. - The difference between the third term (5) and the fourth term (8) is 3. - The difference between the fourth term (8) and the fifth term (12) is 4. - The difference between the fifth term (12) and the sixth term (17) is 5. Thus, the differences are: 1, 2, 3, 4, and 5. This shows that the increases between consecutive terms are not constant; instead, they vary as they increment by 1, which indicates that each term's difference from its predecessor is consistently increasing, but the increases themselves are not the same value. The answer is indicative of the nature of the sequence where the increments are varied and not constant, which is why the choice representing varied increases is correct. The differences clearly demonstrate a

To analyze the differences between the consecutive terms in the given sequence: 2, 3, 5, 8, 12, 17, we can start by calculating the differences:

• The difference between the first term (2) and the second term (3) is 1.

• The difference between the second term (3) and the third term (5) is 2.

• The difference between the third term (5) and the fourth term (8) is 3.

• The difference between the fourth term (8) and the fifth term (12) is 4.

• The difference between the fifth term (12) and the sixth term (17) is 5.

Thus, the differences are: 1, 2, 3, 4, and 5.

This shows that the increases between consecutive terms are not constant; instead, they vary as they increment by 1, which indicates that each term's difference from its predecessor is consistently increasing, but the increases themselves are not the same value.

The answer is indicative of the nature of the sequence where the increments are varied and not constant, which is why the choice representing varied increases is correct. The differences clearly demonstrate a