Question

What is the missing number in the table?

x
1
2
3
4
5
y
6
36
216
???
7,776

252
396
864
1,296

Answer 1

To find the missing number in the table, we can start by analyzing the relationship between the values of \( x \) and \( y \).

Looking at the given \( y \) values:

- For \( x = 1, y = 6 \)
- For \( x = 2, y = 36 \)
- For \( x = 3, y = 216 \)
- For \( x = 4, y = ??? \)
- For \( x = 5, y = 7,776 \)

Let's try to identify a pattern in the \( y \) values with respect to \( x \).

Looking carefully at the values:

1. \( y = 6 = 6 \times 1^1 \)
2. \( y = 36 = 6 \times 6 = 6 \times 6^1 \)
3. \( y = 216 = 6 \times 36 = 6 \times 6^2 \)
4. If we continue with this pattern:
5. \( y = ?? = 6 \times 6^3 \)
6. \( y = 7776 = 6 \times 216 = 6 \times 6^4 \)

We can deduce that \( y = 6 \times 6^{x-1} \).

Now we can calculate the missing \( y \) value for \( x = 4 \):

\[
y = 6 \times 6^{4-1} = 6 \times 6^3 = 6 \times 216 = 1296
\]

So, the missing number in the table when \( x = 4 \) is \( y = 1296 \).