Skill: Determine rules from input-output tables

A rule tells what to do to each input to get its output. To find the rule:

1. Compare the inputs and outputs.
2. Try a simple operation, such as adding, subtracting, multiplying, or dividing.
3. If one operation does not work, try two steps.
4. Check the rule with every pair in the table.
5. Use the rule to find any missing value.

Example:

Input	Output
2	7
4	13
6	19
8	?

First, check whether the same number is added each time:

• $2+5=7$
• But $4+5=9$, not $13$

So adding $5$ is not the rule.

Next, try multiplying by $3$ and then adding $1$:

• $2\times3+1=7$
• $4\times3+1=13$
• $6\times3+1=19$

It works for all the completed rows, so the rule is:

$$\text{Multiply the input by }3\text{, then add }1.$$

Use the rule for an input of $8$:

$$8\times3+1=24+1=25$$

So the missing output is $\boxed{25}$.