The problem shows a sequence of numbers that increases by the same amount each time. We are tasked with finding the three missing terms between 5 and 17.

Step-by-Step Solution:

1. Determine the total increase in the sequence:

   • The difference between the first and last given terms is: $17 - 5 = 12$

2. Divide the total increase evenly:

   • There are four intervals between the terms: $5, \_\_, \_\_, \_\_, 17$.
   • To find the common difference, divide the total increase ($12$) by the number of intervals ($4$): $\text{Common difference} = \frac{12}{4} = 3$

3. Fill in the missing terms:

   • Starting with 5 and adding the common difference ($3$) repeatedly:
     • First missing term: $5 + 3 = 8$
     • Second missing term: $8 + 3 = 11$
     • Third missing term: $11 + 3 = 14$

4. Verify the sequence:

   • Full sequence: $5, 8, 11, 14, 17$.

Final Answer:

The three missing terms are: $8, 11, 14$

Would you like me to explain this further or help with additional examples?

Related Questions:

1. How can you find the common difference in an arithmetic sequence with more terms?
2. What is the formula for the $n$-th term of an arithmetic sequence?
3. How do you determine if a sequence is arithmetic or geometric?
4. Can a sequence have a negative common difference? What would that look like?
5. How can you sum up the terms in an arithmetic sequence efficiently?

Tip:

In arithmetic sequences, the common difference can always be calculated by subtracting any term from the one that follows it!