Complete the patterns below and state the rule: 1.a. 78, 84, 90, 96, ... 1.b. 2, 8, 32, 128, ... 2. Xolile fills up his car's tank with petrol. When full, the tank holds 60 L of petrol. The table belo

The common difference is 6.

The completed pattern is $78, 84, 90, 96, \mathbf{102}$.
The rule is: Add 6 to the previous term.

1.1.b. Complete the patterns below and state the rule:
The given pattern is $2, 8, 32, 128, \dots$

The common ratio is 4.

The completed pattern is $2, 8, 32, 128, \mathbf{512}$.
The rule is: Multiply the previous term by 4.

1.2. Xolile fills up his car's tank with petrol. When full, the tank holds $60 \text{ L}$ of petrol. The table below shows how much petrol is left in the tank as Xolile drives.
Based on this information, how many kilometres can Xolile expect to drive until the petrol tank is completely empty?

From the table:

• For every $40 \text{ km}$ driven ($40 - 0$, $80 - 40$, etc.), the petrol in the tank decreases by $4 \text{ L}$ ($60 - 56$, $56 - 52$, etc.). So, $4 \text{ L}$ of petrol is consumed for every $40 \text{ km}$ driven.

Xolile can expect to drive $\boxed{\text{600 km}}$ until the petrol tank is completely empty.

ACTIVITY 2

2. For his party, Yolanda arranges small square tables in a straight line so that one person sits at each side of the table. For example, if there are 4 tables, then 10 people can sit at the tables, as shown.

• For 1 table: There are 2 people on the long sides and 1 person on each end. So, $2 \times 1 + 2 = 4$ people.
• For 2 tables: There are 2 people on the long sides of each table, but the middle sides are joined. So, $2 \times 2 + 2 = 6$ people.
• For 3 tables: $2 \times 3 + 2 = 8$ people.
• For 4 tables: (Given) 10 people. This matches $2 \times 4 + 2 = 10$.

The pattern shows that for each additional table, 2 more people can be seated. This is an arithmetic progression.
The rule can be expressed as:

Where $P$ is the number of people and $n$ is the number of tables.