Question

Use inductive reasoning to predict the next number in each sequence.

$2,-4,8,-16,\mathrm{....}$

Short answer

Sequence with next number is $2,-4,8,-16,\underset{¯}{32}\mathrm{...}$.

Step-by-step solution

Step 1. Define inductive reasoning.

Inductive reasoning is conclusions based on several past observations.

Step 2. Look for a pattern.

While looking for a pattern in the sequence $2,-4,8,-16,\mathrm{...}$reason inductively that is., we can conclude based on past observations

As,

$\begin{array}{l}{a}_1=2\\ a_2=2\times -2=-4\\ a_3=-4\times -2=8\\ a_4=8\times -2=-16\end{array}$

So, the pattern of the sequence is that every term is getting multiplied by –2 to obtain the next term.

Step 3. Predict the next number of the sequence.

Since the pattern of the sequence is that every term is getting multiplied by –2 to obtain the next term, therefore, the next two terms of the sequence will be,

$a_5=-16\times -2=32$.

Therefore, the sequence will be $2,-4,8,-16,\underset{¯}{32}\mathrm{...}$.