The pattern below follows the 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."

\begin{tabular}{|l|l|}
\hline
& \\
\hline
Row 1 & 3 \\
\hline
Row 2 & 4 \\
\hline
Row 3 & 6 \\
\hline
\end{tabular}

What is the value for the 6th row?

A. 36
B. 18
C. 34
D. 66



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