To find the missing number in the fourth row, let's analyze the patterns in each of the previous rows step-by-step.
### Row 1: [4, 9, 18]
- Look at the transition from 4 to 9 and from 9 to 18:
- 4 [tex]$\rightarrow$[/tex] 9: By inspection, this could be achieved by multiplying 4 by 2 and adding 1.
[tex]\[
4 \times 2 + 1 = 8 + 1 = 9
\][/tex]
- 9 [tex]$\rightarrow$[/tex] 18: Notice that multiplying 9 by 2 equals 18.
[tex]\[
9 \times 2 = 18
\][/tex]
### Row 2: [7, 6, 19]
- Look at the transition from 7 to 6 and from 6 to 19:
- 7 [tex]$\rightarrow$[/tex] 6: This could be achieved by subtracting 1 from 7.
[tex]\[
7 - 1 = 6
\][/tex]
- 6 [tex]$\rightarrow$[/tex] 19: If we triple 6 and add 1, we get 19.
[tex]\[
6 \times 3 + 1 = 18 + 1 = 19
\][/tex]
### Row 3: [15, 22, 30]
- Look at the transition from 15 to 22 and from 22 to 30:
- 15 [tex]$\rightarrow$[/tex] 22: This can be done by adding 7 to 15.
[tex]\[
15 + 7 = 22
\][/tex]
- 22 [tex]$\rightarrow$[/tex] 30: Adding 8 to 22 results in 30.
[tex]\[
22 + 8 = 30
\][/tex]
### Row 4: [165, 330, ?]
- We now try to use the patterns we have seen.
- 165 [tex]$\rightarrow$[/tex] 330: Notice that multiplying 165 by 2 gives us 330.
[tex]\[
165 \times 2 = 330
\][/tex]
Since the patterns observed in other rows are consistent transformations that could apply here (multiplication being commonly used), we continue by applying the same multiplicative pattern down the row:
- Assuming that 330 follows a similar multiplication pattern to yield the missing value:
- Let’s use the consistent pattern of doubling:
[tex]\[
330 \times 2 = 660
\][/tex]
Thus, the missing number in the fourth row is:
[tex]\[
\boxed{660}
\][/tex]
