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."

To analyze the given pattern, we will first establish the initial value and then recursively define the values for each row as per the rule provided.

1. Break Down the Problem

• Start with the initial value: $a_1 = 4$
• Each subsequent value is defined by the rule: $a_n = 2 \cdot a_{n-1} - 2$ for $n \geq 2$

2. Relevant Concepts

• This is a recursive equation where each term depends on its predecessor.

3. Analysis and Detail

• Let's find the first few values:

  • For $a_2$: $a_2 = 2 \cdot a_1 - 2 = 2 \cdot 4 - 2 = 8 - 2 = 6$

  • For $a_3$: $a_3 = 2 \cdot a_2 - 2 = 2 \cdot 6 - 2 = 12 - 2 = 10$

  • For $a_4$: $a_4 = 2 \cdot a_3 - 2 = 2 \cdot 10 - 2 = 20 - 2 = 18$

  • For $a_5$: $a_5 = 2 \cdot a_4 - 2 = 2 \cdot 18 - 2 = 36 - 2 = 34$

4. Verify and Summarize

• The values computed are:
  • $a_1 = 4$
  • $a_2 = 6$
  • $a_3 = 10$
  • $a_4 = 18$
  • $a_5 = 34$

These values confirm the application of the recursive formula aligns with the rule given.

Final Answer

The first five values of the sequence are 4, 6, 10, 18, and 34.