Six learners sit in one table m add another it's 8. How many learners would it take in 200 tables. What is the equation

Let's break this down. 

You mentioned that with **one table**, there are **6 learners**, and by adding another, the total becomes **8 learners**. This suggests that the first table holds **6 learners**, and for every additional table, **2 more learners** are added. This results in a pattern.

Now, let's find the equation for the number of learners, \( L \), based on the number of tables, \( T \).

- For 1 table, \( L = 6 \).
- For 2 tables, \( L = 8 \).
- The increase in learners from the second table onward is 2 learners per table.

### Equation:
The general equation is:

\[
L = 6 + 2(T - 1)
\]

Where:
- \( L \) is the total number of learners.
- \( T \) is the number of tables.

This equation reflects that the first table has 6 learners, and each additional table adds 2 more learners.

### Now, for 200 tables:
Substitute \( T = 200 \) into the equation:

\[
L = 6 + 2(200 - 1) = 6 + 2(199) = 6 + 398 = 404
\]

So, with **200 tables**, there would be **404 learners**.

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Would you like more details or have any questions? Here are 5 related questions to consider:

1. What happens if the number of learners per table changes after the first few tables?
2. How would the equation change if there are different configurations of learners at different tables?
3. Can you generalize this pattern for any number of tables and learners?
4. What if instead of adding 2 learners per table, the number increases by a different amount?
5. How would the solution change if the tables are arranged in different groupings?

**Tip:** Always look for the base value and the rate of change to form equations in situations like this.

This problem explores how to calculate the number of learners at 200 tables using a linear arithmetic sequence. Starting with 6 learners at the first table and increasing by 2 learners per additional table, the final result shows that 404 learners are needed for 200 tables. Learn how to derive the equation L = 6 + 2(T - 1) and apply it step-by-step. Suitable for students in Grades 6-8.

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