Question

Look for a pattern and predict the next two numbers in each sequence.

$18,15,12,9,\mathrm{....}$

Short answer

Sequence with next two numbers is $18,15,12,9,\underset{¯}{6},\underset{¯}{3},\mathrm{...}$.

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 $18,15,12,9,\mathrm{....}$reason inductively that is., we can conclude based on past observations

As,

$\begin{array}{l}18-15=3\\ 15-12=3\\ 12-9=3\end{array}$

So, the pattern of the sequence is that the next term is 3 less 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 3 less than the current term So, the next two term of the sequence will be,

$9-3=6$and $6-3=3$

Therefore, the sequence will be $18,15,12,9,\underset{¯}{6},\underset{¯}{3},\mathrm{...}$.

Therefore, sequence with next two numbers is $18,15,12,9,\underset{¯}{6},\underset{¯}{3},\mathrm{...}$.