Finding Zero in the Sequence: Solve for n in 3n - 3

Q: What does it mean for a number to be 'in' a sequence?

A number is 'in' a sequence if there exists some positive integer position n where the sequence formula gives that number as output.

Q: What if I get a negative or fractional value for n?

Sequence positions must be positive integers (1, 2, 3, ...). If you get a negative number or fraction, then your target value is not in the sequence.

Q: Can the first term of a sequence be zero?

Absolutely! The first term occurs when $ n = 1 $. If substituting $ n = 1 $ into your formula gives zero, then zero is the first term.

Q: Do I always start checking from n = 1?

Yes! Sequences typically start at $ n = 1 $ unless stated otherwise. The first term corresponds to $ n = 1 $, second term to $ n = 2 $, and so on.

Sequence Terms with Zero Values

$3n-3$

Is the number 0 a term in the sequence above?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is the number 0 a member of the sequence?

00:03 We'll substitute the member into the sequence formula and solve for N

00:07 If the solution for N is positive and whole, then this is the member's position

00:12 Let's isolate N

00:25 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

$3n-3$

Is the number 0 a term in the sequence above?

Step-by-step solution

To determine if the number 0 is part of the sequence given by $3n - 3$ , we will follow these steps:

Step 1: Set the sequence expression equal to 0, as follows: $3n - 3 = 0$ .
Step 2: Solve for $n$ by adding 3 to both sides: $3n = 3$ .
Step 3: Divide both sides by 3 to isolate $n$ : $n = 1$ .

Since $n = 1$ is a valid integer, it indicates that the term 0 is indeed part of the sequence. Specifically, 0 is the value of the sequence when $n = 1$ .

Therefore, the number 0 is the first term in the sequence when $n = 1$ . The correct answer is:

Yes, it's the first term.

The correct choice based on the options given is choice 1.

Final Answer

Yes, it's the first term.

Key Points to Remember

Essential concepts to master this topic

Rule: Set sequence expression equal to target value to find position
Technique: Solve $3n - 3 = 0$ gives $n = 1$
Check: Substitute back: $3(1) - 3 = 0$ confirms first term ✓

Common Mistakes

Avoid these frequent errors

Assuming zero cannot be in sequences
Don't think sequences can't contain zero = missing valid solutions! Zero is a perfectly valid term that can appear in any sequence. Always solve the equation completely to check if your target value exists.

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 it mean for a number to be 'in' a sequence?

A number is 'in' a sequence if there exists some positive integer position n where the sequence formula gives that number as output.

How do I find which term number gives me zero?

Set the sequence expression equal to zero and solve for n. If n is a positive integer, then zero appears at that position in the sequence.

What if I get a negative or fractional value for n?

Sequence positions must be positive integers (1, 2, 3, ...). If you get a negative number or fraction, then your target value is not in the sequence.

Can the first term of a sequence be zero?

Absolutely! The first term occurs when $n = 1$ . If substituting $n = 1$ into your formula gives zero, then zero is the first term.

Do I always start checking from n = 1?

Yes! Sequences typically start at $n = 1$ unless stated otherwise. The first term corresponds to $n = 1$ , second term to $n = 2$ , and so on.

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