Question 6 - NUMBER PATTERNS 6.1 Complete the number pattern and describe it in words: 5; 9; 13; 17; PATTERN IN WORDS: 6.2 Consider the matchstick pattern below and complete the table.

On a number line, $-9$ is to the left of $-3$, meaning $-9$ is smaller than $-3$.

• 5.3.1 Calculate $(-7) + (+5)$.

  $$(-7) + (+5) = -7 + 5 = -2$$ $$(-7) + (+5) = \boxed{-2}$$

• 5.3.2 Calculate $(+8) - (-4)$. Subtracting a negative number is equivalent to adding its positive counterpart.

  $$(+8) - (-4) = 8 + 4 = 12$$ $$(+8) - (-4) = \boxed{12}$$

• 5.3.3 Calculate $(-5) + (-6) + (+14) + (-2)$. Combine the negative numbers first:

  $$-5 - 6 - 2 = -13$$

  Then add the positive number:

  $$-13 + 14 = 1$$ $$(-5) + (-6) + (+14) + (-2) = \boxed{1}$$

The temperature inside the freezer is $-18^\circ\text{C}$.
The temperature outside is $16^\circ\text{C}$.
To find the difference, subtract the lower temperature from the higher temperature.

The difference in temperature is $\boxed{34^\circ\text{C}}$.

The given pattern is $5; 9; 13; 17; \_ ; \_$.
Find the common difference between consecutive terms:
$9 - 5 = 4$
$13 - 9 = 4$
$17 - 13 = 4$
The pattern increases by 4 each time.
The next two terms are:
$17 + 4 = 21$
$21 + 4 = 25$
The completed pattern is $5; 9; 13; 17; \boxed{21}; \boxed{25}$.
PATTERN IN WORDS: The pattern starts at 5 and increases by 4 for each subsequent term.

The number of matchsticks for patterns $1, 2, 3$ are $4, 7, 10$.
Find the common difference:
$7 - 4 = 3$
$10 - 7 = 3$
The number of matchsticks increases by 3 for each subsequent pattern.
The rule for the number of matchsticks ($M$) in terms of the pattern number ($n$) is $M = 3n + c$.
Using $n=1, M=4$: $4 = 3(1) + c \implies 4 = 3 + c \implies c = 1$.
So the rule is $M = 3n + 1$.
Now, complete the table for $n=5$ and $n=10$:

• For $n=5$: $M = 3(5) + 1 = 15 + 1 = 16$.
• For $n=10$: $M = 3(10) + 1 = 30 + 1 = 31$.

The completed table is:

Rule: $\boxed{M = 3n + 1}$

The rule is $y = 4x - 3$.

• For $x=0$: $y = 4(0) - 3 = 0 - 3 = -3$.
• For $x=1$: $y = 4(1) - 3 = 4 - 3 = 1$.
• For $x=2$: $y = 4(2) - 3 = 8 - 3 = 5$.
• For $x=3$: $y = 4(3) - 3 = 12 - 3 = 9$.
• For $x=4$: $y = 4(4) - 3 = 16 - 3 = 13$.
• For $x=10$: $y = 4(10) - 3 = 40 - 3 = 37$.

The completed table is:

The operations are: first multiply by 5, then subtract 2.

• For input 3: $3 \times 5 = 15$ $15 - 2 = 13$ So, $A = \boxed{13}$.

• For input 6: $6 \times 5 = 30$ $30 - 2 = 28$ So, $B = \boxed{28}$.

• For input 11: $11 \times 5 = 55$ $55 - 2 = 53$ So, $C = \boxed{53}$.