To solve this problem, we first need to observe the pattern of learners sitting at the tables.

Step 1: Analyze the pattern

• When there is 1 table, 6 learners sit around it.
• When the teacher joins 2 tables, 8 learners sit around the two tables.

From this, we see that the number of learners doesn't simply double when the number of tables doubles. We can infer a formula based on this relationship.

Step 2: Deriving the formula

We can assume the following pattern for calculating the number of learners:

• When there is 1 table, 6 learners sit.
• When there are 2 tables, there are 8 learners. This can be thought of as 6 learners for the first table and 2 more learners for each additional table.

Thus, for T tables:

• The first table accommodates 6 learners.
• Every additional table accommodates 2 extra learners.

So, the formula to calculate the number of learners for any number of tables can be written as: $\text{Number of learners} = 6 + 2(T - 1)$ Where:

• $T$ is the number of tables.
• $T - 1$ accounts for the additional tables beyond the first one, each contributing 2 learners.

Step 3: Calculate for each case

2.4.1: Five tables

Using the formula: $\text{Number of learners} = 6 + 2(5 - 1) = 6 + 2(4) = 6 + 8 = 14$ So, 14 learners can sit at 5 tables.

2.4.2: Twenty-five tables

Using the formula: $\text{Number of learners} = 6 + 2(25 - 1) = 6 + 2(24) = 6 + 48 = 54$ So, 54 learners can sit at 25 tables.

2.4.3: Two hundred tables

Using the formula: $\text{Number of learners} = 6 + 2(200 - 1) = 6 + 2(199) = 6 + 398 = 404$ So, 404 learners can sit at 200 tables.

Summary of answers:

• 2.4.1: 14 learners sit at 5 tables.
• 2.4.2: 54 learners sit at 25 tables.
• 2.4.3: 404 learners sit at 200 tables.

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Would you like further clarification on any of the steps? Here are 5 questions to deepen your understanding:

1. How does the number of learners change as the number of tables increases?
2. Why do only 2 extra learners sit at each additional table after the first one?
3. Can you extend this formula to fractional tables or smaller groups?
4. How would the pattern change if more learners could sit at each table?
5. What would happen if the number of learners per additional table doubled?

Tip: Always try to identify patterns in problems like this to make general formulas easier to derive.