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

Q: What does n represent in the formula?

The variable n represents the position of the term in the sequence. So n = 1 gives the first term, n = 2 gives the second term, and so on.

Q: What type of sequence is 2n - 1?

This is an arithmetic sequence where each term increases by 2. It generates all the odd positive numbers starting from 1.

Q: What if I get confused about which term I'm looking for?

Remember: the term number equals the n value. Second term means n = 2, fifth term means n = 5. Always double-check by counting the position you need!

Sequence Formulas with Term Position Substitution

$2n-1$

What is the second term of the sequence represented above?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find member #2

00:04 Let's substitute the appropriate member's position in the formula and solve

00:16 Always solve multiplication and division before addition and subtraction

00:23 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

$2n-1$

What is the second term of the sequence represented above?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the position $n = 2$ as we're seeking the second term of the sequence.
Step 2: Substitute the value $n = 2$ into the formula $2n - 1$ .
Step 3: Calculate the result of the substitution to find the second term.

Now, let's perform these steps:

Substitute $n = 2$ into the formula:

$2n - 1 = 2(2) - 1$

Simplify the expression:

$= 4 - 1 = 3$

Therefore, the second term of the sequence is $\boldsymbol{3}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Use the general term $2n - 1$ to find any term
Technique: Substitute n = 2 into formula: $2(2) - 1 = 3$
Check: First term is 1, second is 3, third is 5 - pattern increases by 2 ✓

Common Mistakes

Avoid these frequent errors

Using n = 1 instead of n = 2 for the second term
Don't substitute n = 1 when finding the second term = getting 2(1) - 1 = 1! This gives you the first term instead of the second. Always match the term position number with the value of n.

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 does n represent in the formula?

The variable n represents the position of the term in the sequence. So n = 1 gives the first term, n = 2 gives the second term, and so on.

How do I find the first few terms of this sequence?

Substitute consecutive values of n:

n = 1: $2(1) - 1 = 1$
n = 2: $2(2) - 1 = 3$
n = 3: $2(3) - 1 = 5$

The sequence is: 1, 3, 5, 7, ...

What type of sequence is 2n - 1?

This is an arithmetic sequence where each term increases by 2. It generates all the odd positive numbers starting from 1.

Can I use this formula to find any term in the sequence?

Yes! Just substitute the position number for n. Want the 10th term? Use n = 10: $2(10) - 1 = 19$ . The formula works for any positive integer value of n.

What if I get confused about which term I'm looking for?

Remember: the term number equals the n value. Second term means n = 2, fifth term means n = 5. Always double-check by counting the position you need!

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