Find the Position of 18 in the Sequence 4n-2: Term Identification

Question

Given a formula with a constant property that depends onn n :

4n2 4n-2

Is the number 18 Is it part of the series? If so, what element is it in the series?

Video Solution

Solution Steps

00:11 Let's figure out if 8 is part of this sequence. And if so, at what position?
00:16 To find out, we'll plug 8 into our sequence formula and solve it.
00:22 If we get a positive whole number for N, then 8 is in the sequence at position N.
00:27 Okay, let's work to isolate the variable N now.
00:50 And there we go. That's how we solve this question!

Step-by-Step Solution

To determine if the number 18 is part of the series described by the formula an=4n2 a_n = 4n - 2 , follow these steps:

  • Step 1: Set up the equation 4n2=18 4n - 2 = 18 .
  • Step 2: Solve for n n by first adding 2 to both sides: 4n=20 4n = 20 .
  • Step 3: Divide both sides by 4 to isolate n n : n=5 n = 5 .

We have found n=5 n = 5 , which is an integer, indicating that 18 is indeed part of the series 4n2 4n - 2 , where n n is a positive integer. Thus, the element 18 is in the 5th position of the series.

Therefore, the number 18 is part of the series, and it is the 5th element.

The correct answer, based on the choices provided, is: Yes, 5 5 .

Answer

Yes, 5 5