Chapter 1, Problem 1RE

For Exercises 1–4, make reasonable conjectures for the next three numbers or letters in the sequence.

1. 3 4 6 7 9 10 12 13 15 16 ___ ___ ___

To determine

To find: The next three numbers or letters in the sequence by making reasonable conjecture.

Answer to Problem 1RE

The next number in the given sequence is 3 4 6 7 9 10 12 13 15 16 18 19 21.

Explanation of Solution

Result used:

Inductive reasoning is the process of reasoning to a general conclusion through observations of specific cases.

Induction often involves observing a pattern and from that pattern predicting a conclusion.

Calculation:

The sequence is 3 4 6 7 9 10 12 13 15 16.

From the given sequence, it is observed that the difference between the first and the second number is 1.

The difference of second and third number is 2

The difference of third and the fourth number is 1.

Therefore, it can be concluded that the difference of the numbers are changing alternatively by 1 and 2. This is the conjecture for given sequence.

The difference between the tenth and eleventh number in the sequence will be 2 and the required number is 18.

The next difference will be 1 and the next number is 19.

Similarly, the last number is 21.

Thus, the pattern of the sequence is 3 4 6 7 9 10 12 13 15 16 18 19 21.