Final answer:
To find the next number in the given sequence, we can use inductive reasoning by observing the pattern and making an educated prediction.
Step-by-step explanation:
To determine the next number in the sequence 4, 9, 19, 34, 54, 79, we can use inductive reasoning. Inductive reasoning involves making observations or finding patterns in a given sequence to make a generalization or prediction.
If we look closely at the given sequence, we can see that the numbers are increasing by a specific pattern.
In this case, we can observe that the differences between consecutive terms in the sequence are increasing by 5 each time. The differences between consecutive terms are 5, 10, 15, 20, and so on.
Therefore, to find the next number in the sequence, we can add 25 to the previous number. The last number in the sequence is 79, so the next number will be 79 + 25 = 104.