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

Q: What if I get a negative or fractional value for n?

If n is negative or a fraction, then the number is not in the sequence! Sequence positions must be positive integers (1, 2, 3, 4...).

Q: Do I need to list out all the sequence terms to check?

No! That would take forever for large numbers. Instead, solve algebraically by setting $ 2n - 1 = \text{target number} $ and checking if n is a positive integer.

Q: Can I use this method for any sequence expression?

Yes! For any sequence defined by an expression like $ 3n + 2 $ or $ n^2 - 1 $, just set it equal to your target number and solve for n.

Sequence Membership with Algebraic Verification

$2n-1$

Is the number 15 an element in the sequence above?

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Step-by-step video solution

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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 written solution

Follow each step carefully to understand the complete solution

Understand the problem

$2n-1$

Is the number 15 an element in the sequence above?

Step-by-step solution

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

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

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

$2n = 16$

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

$n = 8$

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

Therefore, the correct answer is Yes.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Definition: Set sequence expression equal to target number to test membership
Technique: Solve $2n - 1 = 15$ by adding 1 then dividing by 2
Check: Verify n = 8 gives positive integer for sequence position ✓

Common Mistakes

Avoid these frequent errors

Assuming 15 isn't in the sequence without solving
Don't guess based on looking at first few terms like 1, 3, 5, 7... = missing later terms! This leads to wrong conclusions about larger numbers. Always solve the equation 2n - 1 = target number to verify membership.

Practice Quiz

Test your knowledge with interactive questions

Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

FAQ

Everything you need to know about this question

What if I get a negative or fractional value for n?

If n is negative or a fraction, then the number is not in the sequence! Sequence positions must be positive integers (1, 2, 3, 4...).

Do I need to list out all the sequence terms to check?

No! That would take forever for large numbers. Instead, solve algebraically by setting $2n - 1 = \text{target number}$ and checking if n is a positive integer.

How do I know what the sequence 2n-1 looks like?

Substitute values: n=1 gives 1, n=2 gives 3, n=3 gives 5, etc. This creates the odd numbers sequence: 1, 3, 5, 7, 9, 11, 13, 15...

What if the equation doesn't solve evenly?

If you get something like n = 7.5, then the target number is not in the sequence. Only whole number values of n produce valid sequence elements.

Can I use this method for any sequence expression?

Yes! For any sequence defined by an expression like $3n + 2$ or $n^2 - 1$ , just set it equal to your target number and solve for n.

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