Find the Fifth Term in the Sequence 2n-1: Step-by-Step Solution

Q: What does n represent in the formula 2n - 1?

n represents the position of the term in the sequence. For the first term, n = 1. For the fifth term, n = 5. It's not the value of the term itself.

Q: Why is this called an arithmetic sequence?

It's arithmetic because there's a constant difference between consecutive terms. Each term increases by 2: 1→3→5→7→9. The common difference is 2.

Q: Can I use this formula to find any term?

Absolutely! Just substitute the position number for n. Want the 10th term? Calculate $ 2(10) - 1 = 19 $. Want the 100th term? Calculate $ 2(100) - 1 = 199 $.

Arithmetic Sequences with Formula Substitution

For the series $2n-1$

What is the fifth element?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the fifth term in the sequence

00:03 Substitute N = 5 in the sequence formula

00:12 Substitute and solve to find the term

00:20 Always solve multiplication and division before addition and subtraction

00:26 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

For the series $2n-1$

What is the fifth element?

Step-by-step solution

The sequence given is defined by the formula $2n - 1$ . To find the fifth element, we substitute $n = 5$ into the formula.

Following these steps:

Substitute $n = 5$ into the formula: $a_5 = 2(5) - 1$ .
Perform the calculation: $2 \times 5 = 10$ , and then $10 - 1 = 9$ .

Thus, the fifth element of the series is $9$ .

Therefore, the solution to this problem is $\mathbf{9}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Substitute the term position into the sequence formula
Calculation: For fifth term, $2(5) - 1 = 10 - 1 = 9$
Verification: Check by computing first few terms: 1, 3, 5, 7, 9 ✓

Common Mistakes

Avoid these frequent errors

Confusing the term position with the term value
Don't substitute n = 9 to find the fifth term = you'll get 2(9) - 1 = 17! This confuses the answer with the position. Always substitute the position number (n = 5) into the formula.

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 does n represent in the formula 2n - 1?

n represents the position of the term in the sequence. For the first term, n = 1. For the fifth term, n = 5. It's not the value of the term itself.

How can I check if my answer is correct?

Calculate the first few terms to see the pattern: $n=1: 2(1)-1=1$ , $n=2: 2(2)-1=3$ , $n=3: 2(3)-1=5$ . The sequence should be 1, 3, 5, 7, 9...

Why is this called an arithmetic sequence?

It's arithmetic because there's a constant difference between consecutive terms. Each term increases by 2: 1→3→5→7→9. The common difference is 2.

Can I use this formula to find any term?

Absolutely! Just substitute the position number for n. Want the 10th term? Calculate $2(10) - 1 = 19$ . Want the 100th term? Calculate $2(100) - 1 = 199$ .

What if I accidentally use the wrong value for n?

Always double-check what the question is asking! If it says 'fifth term', then n = 5. If it says 'tenth term', then n = 10. The term position equals your n value.

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