Find If 5 Is in the Arithmetic Sequence: Solve 2n - 1

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

If n is negative, the number is not in the sequence! Sequence positions must be positive integers (1, 2, 3, ...), so negative n values mean the target number doesn't exist in the sequence.

Q: What if n comes out as a fraction like 2.5?

Fractional n values mean the number is not a term in the sequence. Since we can't have position 2.5 in a sequence, only whole number positions count!

Q: How do I know which equation to set up?

Set the sequence formula equal to your target number. For $ 2n - 1 $ and target 5, write: $ 2n - 1 = 5 $

Q: Can I just plug in numbers instead?

You could try $ n = 1, 2, 3... $ but solving algebraically is much faster! Plus, if the number isn't in the sequence, you'd never know when to stop guessing.

Q: What does the sequence 2n - 1 actually generate?

This generates odd numbers: when n = 1, 2, 3, 4... you get 1, 3, 5, 7... So we're checking if 5 appears in this pattern of odd numbers.

Arithmetic Sequence with Term Verification

$2n-1$

Is the number 5 a term in the above sequence?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Is the number 5 part of the sequence?

00:10 We'll plug 5 into the sequence formula, and solve for N.

00:15 If N is a positive whole number, it tells us the position of 5.

00:21 Let's focus on solving for N now.

00:36 Great! That's how we find our answer.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$2n-1$

Is the number 5 a term in the above sequence?

Step-by-step solution

To determine if the number 5 is a term in the sequence given by $a_n = 2n - 1$ , we need to find a positive integer $n$ such that $2n - 1 = 5$ .

Let's solve the equation:

1. Start with the equation: $2n - 1 = 5$

2. Add 1 to both sides to isolate the term involving $n$ : $2n = 6$

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

Since $n = 3$ is a positive integer, the number 5 is indeed a term in the sequence. Therefore, the correct answer is Yes.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Formula: Set sequence formula equal to target value to find n
Technique: Solve $2n - 1 = 5$ gives $n = 3$
Check: Substitute back: $2(3) - 1 = 5$ confirms answer ✓

Common Mistakes

Avoid these frequent errors

Forgetting to check if n is a positive integer
Don't stop after solving for n without checking if it's positive = accepting impossible term positions! Negative or fractional values of n don't represent valid positions in sequences. Always verify n is a positive whole number.

Practice Quiz

Test your knowledge with interactive questions

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

FAQ

Everything you need to know about this question

What if I get a negative value for n?

If n is negative, the number is not in the sequence! Sequence positions must be positive integers (1, 2, 3, ...), so negative n values mean the target number doesn't exist in the sequence.

What if n comes out as a fraction like 2.5?

Fractional n values mean the number is not a term in the sequence. Since we can't have position 2.5 in a sequence, only whole number positions count!

How do I know which equation to set up?

Set the sequence formula equal to your target number. For $2n - 1$ and target 5, write: $2n - 1 = 5$

Can I just plug in numbers instead?

You could try $n = 1, 2, 3...$ but solving algebraically is much faster! Plus, if the number isn't in the sequence, you'd never know when to stop guessing.

What does the sequence 2n - 1 actually generate?

This generates odd numbers: when n = 1, 2, 3, 4... you get 1, 3, 5, 7... So we're checking if 5 appears in this pattern of odd numbers.

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