The pattern below follows the rule: "Starting with a value of 4, every consecutive row has a value that is 2 less than twice the value of the previous row."

\begin{tabular}{|l|l|}
\hline
& \multicolumn{1}{|c|}{Value} \\
\hline
Row 1 & 4 \\
\hline
Row 2 & 6 \\
\hline
Row 3 & 10 \\
\hline
\end{tabular}

What is the value for the 5th row?

A. 20
B. 66
C. 34
D. 36



Answer :

Let's follow the rule to determine the values of each consecutive row, starting with a value of 4 for Row 1.

1. Row 1: The value is given as 4.

2. Row 2: According to the rule, the value for Row 2 is calculated as [tex]\( 2 \times \)[/tex] value of Row 1 [tex]\(- 2 \)[/tex].
[tex]\[ 2 \times 4 - 2 = 8 - 2 = 6 \][/tex]

3. Row 3: Using the same rule for Row 3, the value is [tex]\( 2 \times \)[/tex] value of Row 2 [tex]\(- 2 \)[/tex].
[tex]\[ 2 \times 6 - 2 = 12 - 2 = 10 \][/tex]

Now we need to continue the pattern to find the values for Row 4 and Row 5:

4. Row 4: Following the rule, the value for Row 4 is [tex]\( 2 \times \)[/tex] value of Row 3 [tex]\(- 2 \)[/tex].
[tex]\[ 2 \times 10 - 2 = 20 - 2 = 18 \][/tex]

5. Row 5: Finally, applying the rule to Row 5, the value is [tex]\( 2 \times \)[/tex] value of Row 4 [tex]\(- 2 \)[/tex].
[tex]\[ 2 \times 18 - 2 = 36 - 2 = 34 \][/tex]

Therefore, the value for the 5th row is [tex]\(\boxed{34}\)[/tex].