Evaluate 2(2n-2): Finding the Position of 20 in the Sequence

To determine if the number 20 is part of the sequence given by the formula $2(2n-2)$, we proceed as follows:

• Step 1: Set up the equation, $2(2n-2) = 20$.
• Step 2: Simplify the equation:
  $2(2n-2) = 4n - 4$, thus we have $4n - 4 = 20$.
• Step 3: Solve for $n$:
  Add 4 to both sides: $4n - 4 + 4 = 20 + 4$ gives $4n = 24$.
  Divide both sides by 4: $n = \frac{24}{4} = 6$.
• Step 4: Check if $n$ is a positive integer.
  $n = 6$ is indeed a positive integer.

Since $n = 6$ is a positive integer, 20 is indeed part of the sequence, and it is the 6th term.

Therefore, the solution to the problem is Yes, 6.