Question

The tables for a party are seated as 4 people at 1 table, 6 people at 2 tables, and 8 people at 3 tables. Use a sequence to determine how many tables would be needed for 16 people

Answer 1

To determine how many tables would be needed for 16 people based on the information provided, we can establish a pattern from the given seating arrangements.

From the information provided:

- At **1 table**, there are **4 people**.
- At **2 tables**, there are **6 people**.
- At **3 tables**, there are **8 people**.

We can summarize the arrangements as follows:

- **1 table**: 4 people (1 * 4 = 4)
- **2 tables**: 6 people (2 * 3 = 6)
- **3 tables**: 8 people (3 * 2.67 ≈ 8)

We can create a sequence based on the number of tables and the number of people they accommodate. Let's extract the pattern from the number of people seated:

1. For **4 people at 1 table**: **1 table**
2. For **6 people at 2 tables**: **2 tables**
3. For **8 people at 3 tables**: **3 tables**

Notice that the seating increases by 2 people for every additional table.

We can observe this as:
- Table 1: 4 people
- Table 2: 6 people
- Table 3: 8 people
- And if we extend this logic:

Following the same logic, we could assume the next increments maintain the pattern of adding 2 additional people:
- Table 4: 10 people (4 tables)
- Table 5: 12 people (5 tables)
- Table 6: 14 people (6 tables)
- Table 7: 16 people (7 tables)

From this sequence, we see that it would take **7 tables** to seat **16 people**.

Thus, to accommodate **16 people**, you would need **7 tables**.