Study the pattern below and answer the question that follows. Draw a table to represent stage 1 to stage 5. Describe the pattern in Question 7.1 in your own words

• Stage 1: 2 shaded diamonds
• Stage 2: 4 shaded diamonds
• Stage 3: 6 shaded diamonds
• Stage 4: 8 shaded diamonds The number of shaded diamonds increases by 2 for each subsequent stage. This means the number of diamonds is $2 \times \text{stage number}$.

For stage 5, the number of diamonds will be $2 \times 5 = 10$.

The given numbers are 5, 8, 11, 14.
The differences are:
$8 - 5 = 3$
$11 - 8 = 3$
$14 - 11 = 3$
The common difference $d = 3$.

Here, $a = 5$ and $d = 3$.
Substitute these values into the formula:

The relationship is \boxed{\textbf{T_n = 3n + 2}}.

We need to find the $20^{th}$ number, so substitute $n = 20$ into the rule.

The $20^{th}$ number is $\boxed{\textbf{62}}$.