Find a formula which gives the number of matches, S, required to construct n diagram.

Diagram 1 has 8 matches
Diagram 2 has 15 matches
Diagram 3 has 22 matches

Looks like 7n+1

To find a formula that gives the number of matches required to construct n diagrams, we can observe the given information and look for a pattern.

Given:
- Diagram 1 has 8 matches
- Diagram 2 has 15 matches
- Diagram 3 has 22 matches

Let's analyze the difference between each consecutive diagram:
- Difference between Diagram 1 and Diagram 2: 15 - 8 = 7
- Difference between Diagram 2 and Diagram 3: 22 - 15 = 7

We can see that the difference between each consecutive diagram is constant, specifically 7 matches. This means that for each additional diagram, we need to add 7 more matches.

Based on this observation, we can set up a formula to calculate the number of matches, S, required to construct n diagrams as follows:

S = 8 + (n - 1) * 7

Explanation of the formula:
- The initial number of matches, 8, represents the matches needed for Diagram 1.
- The term (n - 1) * 7 calculates the additional matches needed for Diagrams 2, 3, 4, and so on. (n - 1) represents the number of additional diagrams, and we multiply it by 7 since each additional diagram requires 7 more matches.

Using this formula, we can easily calculate the number of matches required for any given number of diagrams.