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

00:05 First, let's find member number two.

00:09 Now, substitute the position into the formula and solve it step by step.

00:21 Always remember to do multiplication and division before you add or subtract.

00:28 And that's how we find 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

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?

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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