Determine the value of a, b and c in the following flow diagram and complete the table below: P = 5Q + 2

$7 - 4 = 3$
$10 - 7 = 3$
$13 - 10 = 3$
The common difference is 3.

5.1.1) Write down the next term of the pattern.

Next term $= 13 + 3 = 16$.
The next term is $\boxed{\text{16}}$.

5.1.2) What rule did you use to find the next term of the pattern?

The rule used is to add 3 to the previous term.

5.1.3) Find term 10 of the pattern.

Here, $a = 4$ (first term), $d = 3$ (common difference), and $n = 10$.

$$T_{10} = 4 + (10-1) \times 3$$ $$T_{10} = 4 + 9 \times 3$$ $$T_{10} = 4 + 27$$ $$T_{10} = 31$$

Term 10 is $\boxed{\text{31}}$.

Question 5.2:
Study the Geometric pattern below.
Pattern 1: 1 triangle, 3 matches
Pattern 2: 2 triangles, 5 matches
Pattern 3: 3 triangles, 7 matches

5.2.1) Draw pattern 4.

The number of matches increases by 2 for each new pattern ($5-3=2$, $7-5=2$).
So, Pattern 4 will have $7 + 2 = 9$ matches.
Pattern 4 consists of 4 triangles arranged in a row, sharing one side between adjacent triangles, using 9 matches.

5.2.2) Describe the rule of the pattern in your own words.

The rule is to add 2 matches to the previous pattern to form the next pattern.

Question 6.1:
Determine the value of a, b and c in the following flow diagram.
Input $\rightarrow +3 \rightarrow$ Output

For 'a', the input is 12.

$$a = 12 + 3$$ $$a = 15$$

The value of a is $\boxed{\text{15}}$.

For 'b', the output is 21.

$$b + 3 = 21$$ $$b = 21 - 3$$ $$b = 18$$

The value of b is $\boxed{\text{18}}$.

For 'c', the input is -3.

$$c = -3 + 3$$ $$c = 0$$

The value of c is $\boxed{\text{0}}$.

Question 6.2:
Use the following formula to complete the table below: $P = 5Q + 2$

$$P = 5(2) + 2$$ $$P = 10 + 2$$ $$P = 12$$

$$P = 5(3) + 2$$ $$P = 15 + 2$$ $$P = 17$$

$$37 = 5Q + 2$$ $$37 - 2 = 5Q$$ $$35 = 5Q$$ $$Q = \frac{35}{5}$$ $$Q = 7$$

$$P = 5(10) + 2$$ $$P = 50 + 2$$ $$P = 52$$

The completed table is:
Input (Q) | 1 | 2 | 3 | 7 | | 10
Output (P)| 7 | 12 | 17 | 37 | | 52
The values to complete the table are $\boxed{\text{P=12 (for Q=2), P=17 (for Q=3), Q=7 (for P=37), P=52 (for Q=10)}}$.