Question

Use inductive reasoning to predict the next two numbers in each sequence.

15, 30, 45, 60, ...

Short answer

Sequence with next two numbers is 15, 30, 45, 60, _75, _90, ...

Step-by-step solution

Step 1. Define deductive and inductive reasoning.

Deductive reasoning is conclusions based on accepted statements like a theorem, postulate, facts etc.

Inductive reasoning is conclusions based on several past observations.

Step 2. Look for a pattern.

While looking for a pattern in the sequence 15, 30, 45, 60, ... reason inductively that is., we can conclude based on past observations

As,

15 + 15 = 30

30 + 15 = 45

45 + 15 = 60

So, the pattern of the sequence is that the next term is 15 more than the current term.

Step 3. Predict the next two numbers of the sequence.

Since, the pattern of the sequence is that the next term is 15 more than the current term So, the next two term of the sequence will be,

60 + 15 = 75 and 75 + 15 = 90.

Therefore, sequence with next two numbers is 15, 30, 45, 60, _75, _90, ...