Sequence Expression 2n-1: Is 15 a Valid Element?

Question

2n1 2n-1

Is the number 15 an element in the sequence above?

Video Solution

Solution Steps

00:00 Is the number 15 a member of the sequence?
00:03 Let's substitute the number into the formula and solve
00:09 If N results in a whole number, the number is a member of the sequence
00:13 Let's isolate N
00:32 This is the position of the member in the sequence, and this is the solution to the question

Step-by-Step Solution

To determine if 15 is an element of the sequence defined by 2n1 2n - 1 , follow these steps:

  • Step 1: Set the equation 2n1=15 2n - 1 = 15 .
  • Step 2: Solve the equation for n n .

Let's work through the solution:
Step 1: Start with the equation 2n1=15 2n - 1 = 15 .
Step 2: Add 1 to both sides of the equation to isolate the term with n n :

2n=16 2n = 16

Step 3: Divide both sides by 2 to solve for n n :

n=8 n = 8

Since n=8 n = 8 is a positive integer, 15 is indeed part of the sequence described by 2n1 2n - 1 .

Therefore, the correct answer is Yes.

Answer

Yes