Answer :
Let's analyze the given pattern step-by-step based on the provided rule: "starting with a value of 3, every consecutive row has a value that is 2 less than twice the value of the previous row."
1. Row 1: The value is given as 3.
[tex]\[ \text{Row 1 value} = 3 \][/tex]
2. Row 2: To find Row 2, we use the given rule: [tex]\(2 \times \text{Row 1 value} - 2\)[/tex].
[tex]\[ \text{Row 2 value} = 2 \times 3 - 2 = 6 - 2 = 4 \][/tex]
3. Row 3: To find Row 3, we use the same rule with the value of Row 2:
[tex]\[ \text{Row 3 value} = 2 \times 4 - 2 = 8 - 2 = 6 \][/tex]
4. Row 4: Continuing the pattern with the value from Row 3:
[tex]\[ \text{Row 4 value} = 2 \times 6 - 2 = 12 - 2 = 10 \][/tex]
5. Row 5: Using the value from Row 4:
[tex]\[ \text{Row 5 value} = 2 \times 10 - 2 = 20 - 2 = 18 \][/tex]
6. Row 6: Finally, using the value from Row 5 to find Row 6:
[tex]\[ \text{Row 6 value} = 2 \times 18 - 2 = 36 - 2 = 34 \][/tex]
Thus, the value for the 6th row is:
[tex]\[ \boxed{34} \][/tex]
Therefore, the correct answer is:
C. 34
1. Row 1: The value is given as 3.
[tex]\[ \text{Row 1 value} = 3 \][/tex]
2. Row 2: To find Row 2, we use the given rule: [tex]\(2 \times \text{Row 1 value} - 2\)[/tex].
[tex]\[ \text{Row 2 value} = 2 \times 3 - 2 = 6 - 2 = 4 \][/tex]
3. Row 3: To find Row 3, we use the same rule with the value of Row 2:
[tex]\[ \text{Row 3 value} = 2 \times 4 - 2 = 8 - 2 = 6 \][/tex]
4. Row 4: Continuing the pattern with the value from Row 3:
[tex]\[ \text{Row 4 value} = 2 \times 6 - 2 = 12 - 2 = 10 \][/tex]
5. Row 5: Using the value from Row 4:
[tex]\[ \text{Row 5 value} = 2 \times 10 - 2 = 20 - 2 = 18 \][/tex]
6. Row 6: Finally, using the value from Row 5 to find Row 6:
[tex]\[ \text{Row 6 value} = 2 \times 18 - 2 = 36 - 2 = 34 \][/tex]
Thus, the value for the 6th row is:
[tex]\[ \boxed{34} \][/tex]
Therefore, the correct answer is:
C. 34
