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 find: The next three numbers or letters in the sequence by making reasonable conjecture.
Answer:
The next number in the given sequence is 3 4 6 7 9 10 12 13 15 16 18 19 21.
Explanation:
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.