Determine the First Three Terms of the Sequence: 3n + 3

Q: Why do we start with n=1 instead of n=0?

In most sequence problems, n represents the position of the term, starting from 1. The first term corresponds to n=1, second term to n=2, and so on.

Q: How do I know if I calculated the terms correctly?

Check that each term follows the pattern! For $ 3n+3 $, each term should be 3 more than the previous term: 6→9→12.

Q: What if the sequence formula looks different?

The method stays the same! Just substitute n=1, 2, 3... into whatever formula you're given, whether it's $ 2n-1 $, $ n^2+1 $, or any other expression.

Q: What's the difference between arithmetic and other sequences?

Arithmetic sequences have a constant difference between consecutive terms. Here, the difference is always 3, making this an arithmetic sequence.

Arithmetic Sequences with Linear Expressions

What are the first three elements of the sequence described below?

$3n+3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the first 3 terms

00:04 Substitute the desired term position in the sequence formula and solve

00:18 Always solve multiplication and division before addition and subtraction

00:23 This is the first term in the sequence

00:26 We'll use the same method to find the next terms

00:32 Substitute the desired term position in the sequence formula and solve

00:36 Always solve multiplication and division before addition and subtraction

00:40 This is the second term in the sequence

00:46 Substitute the desired term position in the sequence formula and solve

00:51 Always solve multiplication and division before addition and subtraction

01:01 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

What are the first three elements of the sequence described below?

$3n+3$

Step-by-step solution

We need to find the first three elements of a sequence defined by the equation $3n + 3$ . Here, $n$ is a positive integer. We start by using $n = 1, 2, 3$ to find the corresponding sequence elements.

For $n = 1$ :
Calculate $3(1) + 3 = 3 + 3 = 6$ .
For $n = 2$ :
Calculate $3(2) + 3 = 6 + 3 = 9$ .
For $n = 3$ :
Calculate $3(3) + 3 = 9 + 3 = 12$ .

Therefore, the first three elements of the sequence are 6, 9, and 12.

The correct choice among the given options that matches our calculated result is :

6, 9, 12

Final Answer

6, 9, 12

Key Points to Remember

Essential concepts to master this topic

Rule: Substitute consecutive positive integers starting with n=1
Technique: Calculate 3(1)+3=6, 3(2)+3=9, 3(3)+3=12
Check: Verify pattern: each term increases by 3 ✓

Common Mistakes

Avoid these frequent errors

Starting with n=0 instead of n=1
Don't start with n=0 giving 3, 6, 9 = wrong sequence! Sequences typically begin with the first term at n=1 unless specified otherwise. Always start with n=1 for the first term.

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

Why do we start with n=1 instead of n=0?

In most sequence problems, n represents the position of the term, starting from 1. The first term corresponds to n=1, second term to n=2, and so on.

How do I know if I calculated the terms correctly?

Check that each term follows the pattern! For $3n+3$ , each term should be 3 more than the previous term: 6→9→12.

What if the sequence formula looks different?

The method stays the same! Just substitute n=1, 2, 3... into whatever formula you're given, whether it's $2n-1$ , $n^2+1$ , or any other expression.

Can I find any term in the sequence?

Yes! To find the 10th term, substitute n=10 into the formula: $3(10)+3 = 33$ . This formula works for any position.

What's the difference between arithmetic and other sequences?

Arithmetic sequences have a constant difference between consecutive terms. Here, the difference is always 3, making this an arithmetic sequence.

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