Find the Sixth Term in the Sequence 3n-3: Linear Expression Problem

Q: What does the 'n' represent in the formula?

The n represents the position of the term in the sequence. So for the 6th term, n = 6, for the 10th term, n = 10, and so on.

Q: Why do we get 0 for the first term?

When n = 1: $ 3(1) - 3 = 0 $. This is correct! Some sequences start with 0, and that's perfectly normal in mathematics.

Q: Can I just add 3 to each term to find the next one?

Yes! This sequence increases by 3 each time (0, 3, 6, 9, 12, 15...). But using the formula $ 3n - 3 $ is more reliable, especially for terms far in the sequence.

Sequence Terms with Substitution Method

$3n-3$

What is the sixth term in the sequence?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find the sixth term.

00:09 Substitute the number six into the formula. Then, let's solve it together.

00:22 Remember, multiply and divide before adding and subtracting.

00:31 And that's how we solve it. Great job!

Step-by-step written solution

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Understand the problem

$3n-3$

What is the sixth term in the sequence?

Step-by-step solution

The problem asks us to find the sixth term in the sequence defined by $3n - 3$ .

To solve this problem, we'll use the following steps:

Step 1: Identify the sequence formula, which is $a_n = 3n - 3$ .
Step 2: Determine which term we need, which is the sixth term, so $n = 6$ .
Step 3: Substitute $n = 6$ into the formula.
Step 4: Calculate the result.

Now, let's work through these steps:

Step 1: We have the formula for the sequence as $a_n = 3n - 3$ .

Step 2: We need to find the sixth term, so $n = 6$ .

Step 3: Substitute $n = 6$ into the formula:

$a_6 = 3(6) - 3$

Step 4: Perform the calculation:

$a_6 = 18 - 3 = 15$

Therefore, the sixth term in the sequence is 15.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Use $a_n = 3n - 3$ where n is the term position
Technique: Substitute n = 6 into formula: $3(6) - 3 = 15$
Check: Verify by calculating first few terms: 0, 3, 6, 9, 12, 15 ✓

Common Mistakes

Avoid these frequent errors

Using the formula value as the term number
Don't think that 3n - 3 means the 3rd term minus 3 = wrong answer! This confuses the formula with position. Always substitute the position number (n = 6) into the entire expression 3n - 3.

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 the 'n' represent in the formula?

The n represents the position of the term in the sequence. So for the 6th term, n = 6, for the 10th term, n = 10, and so on.

How do I know which number to substitute for n?

Look at what the question is asking! If it says "sixth term," then n = 6. If it says "tenth term," then n = 10. The term number equals the n value.

Why do we get 0 for the first term?

When n = 1: $3(1) - 3 = 0$ . This is correct! Some sequences start with 0, and that's perfectly normal in mathematics.

Can I just add 3 to each term to find the next one?

Yes! This sequence increases by 3 each time (0, 3, 6, 9, 12, 15...). But using the formula $3n - 3$ is more reliable, especially for terms far in the sequence.

What if I need to find a term like the 100th term?

The formula method is perfect for this! Just substitute n = 100: $3(100) - 3 = 297$ . Much easier than counting up 100 terms!

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