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

Given a formula with a constant property that depends on $n$ :

$2(2n-2)$

Is the number 20 Is it part of the series? If so, what element is it in the series?

Video Solution

Solution Steps

00:00 Is the number 20 a term in the sequence? And if so, what is its position?

00:03 Let's place the desired term in the sequence formula and solve

00:08 If the solution for N is positive and whole, the number is a term at position N in the sequence

00:13 Let's minimize as much as possible

00:22 Let's isolate N

00:39 And this is the solution to the question

Step-by-Step Solution

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.