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 analyze how many tables would be needed for 16 people based on the given seating arrangements, we can first establish a sequence based on the provided data:

1. **1 table → 4 people**
2. **2 tables → 6 people** (total = 4 + 6 = 10 people)
3. **3 tables → 8 people** (total = 10 + 8 = 18 people)

Now, let's calculate the total numbers of attendees for each case:

- For 1 table, the total is 4 people.
- For 2 tables, the total number of people is \( 4 + 6 = 10 \).
- For 3 tables, the total number of people is \( 10 + 8 = 18 \).

Looking at the arrangement, we notice:

- Each increase in the number of tables contributes a certain number of additional guests.
- The pattern in the number of people seated per table appears to be increasing systematically, specifically, adding 2 more people for each 'table group.'

Now, summarizing the total number of people from 1 to 3 tables:
- Table 1 → 4 people
- Table 2 → 10 people (4 from the first table + 6 from the second table)
- Table 3 → 18 people (10 from the first two tables + 8 from the third table)

Next, we need to determine how many tables would accommodate exactly 16 people.

- After observing that 16 people fall between 10 and 18, it indicates that we would require the use of 3 tables.

We've organized it into floors:
- **3 tables can seat a total of 18 people**, which accommodates our needs for **16 people** comfortably.

Thus, the answer is that **3 tables would be needed for 16 people**.