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Complete the patterns below and state the rule. Also, calculate the distance Xolile can drive with a full tank of 60L.

Mathematics

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ACTIVITY 1

1.1.a. Complete the patterns below and state the rule:
The given pattern is 78,84,90,96,102‾78, 84, 90, 96, \underline{\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 2,8,32,128,512‾2, 8, 32, 128, \underline{\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 L60 \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?

  1. Calculate the petrol consumed per distance.

    From the table, for every 40 km40 \text{ km} driven, 4 L4 \text{ L} of petrol is consumed (60−56=4 L60 - 56 = 4 \text{ L}, 56−52=4 L56 - 52 = 4 \text{ L}, etc.).

  2. Determine the fuel efficiency.

    Fuel efficiency=40 km4 L=10 km/L\text{Fuel efficiency} = \frac{40 \text{ km}}{4 \text{ L}} = 10 \text{ km/L}

  3. Calculate the total distance for a full tank (60 L60 \text{ L}).

    Total distance=60 L×10 km/L=600 km\text{Total distance} = 60 \text{ L} \times 10 \text{ km/L} = 600 \text{ km}

    Xolile can expect to drive 600 km\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.

    To represent the pattern, we can create a table showing the number of people for different numbers of tables:

    Number of Tables (n)Number of People (P)142638410512\begin{array}{|c|c|} \hline \textbf{Number of Tables (n)} & \textbf{Number of People (P)} \\ \hline 1 & 4 \\ \hline 2 & 6 \\ \hline 3 & 8 \\ \hline 4 & 10 \\ \hline 5 & 12 \\ \hline \end{array}

  4. Analyze the pattern in the table.

    As the number of tables increases by 1, the number of people increases by 2.

  5. Determine the rule.

    The rule for the number of people (PP) based on the number of tables (nn) is:

    P=2n+2P = 2n + 2
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