Solve the Series Challenge: Completing the Third Term in n-3 Sequence

Q: What does n represent in the expression n - 3?

n represents the position number of the term in the sequence. For the first term, n = 1; for the second term, n = 2; for the third term, n = 3, and so on.

Q: Why isn't the third term equal to 3?

The third term isn't 3 because we need to substitute the position number into the formula. The formula is $ n - 3 $, so the third term is $ 3 - 3 = 0 $.

Q: How do I find any term in this sequence?

Simply substitute the position number for n in the expression $ n - 3 $. For example: 1st term = 1 - 3 = -2, 2nd term = 2 - 3 = -1, 3rd term = 3 - 3 = 0.

Q: What if I get a negative number as an answer?

That's completely normal! Sequences can have negative terms. In this sequence, the first two terms are actually negative: -2 and -1.

Sequence Terms with Substitution Method

For the series $n-3$

Complete the third term.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the third element of the sequence.

00:08 We substitute the position into the sequence formula and solve step by step.

00:27 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

For the series $n-3$

Complete the third term.

Step-by-step solution

To solve for the third term in the series defined by $n - 3$ , we follow these straightforward steps:

Step 1: Identify the expression for the series term, which is $n - 3$ .
Step 2: Substitute $n = 3$ into the expression. This corresponds to finding the third term.
Step 3: Substituting gives us $3 - 3$ , which simplifies to $0$ .

Thus, the third term of the series is $0$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: For term n in expression, substitute n into formula
Technique: For third term, substitute n = 3: (3) - 3 = 0
Check: Verify by counting position: first term n=1, second n=2, third n=3 ✓

Common Mistakes

Avoid these frequent errors

Confusing term position with term value
Don't think the third term equals 3 because it's in third position = wrong answer! The position number (n) gets substituted into the formula, not used as the final answer. Always substitute the position number into the given expression.

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 expression n - 3?

n represents the position number of the term in the sequence. For the first term, n = 1; for the second term, n = 2; for the third term, n = 3, and so on.

Why isn't the third term equal to 3?

The third term isn't 3 because we need to substitute the position number into the formula. The formula is $n - 3$ , so the third term is $3 - 3 = 0$ .

How do I find any term in this sequence?

Simply substitute the position number for n in the expression $n - 3$ . For example: 1st term = 1 - 3 = -2, 2nd term = 2 - 3 = -1, 3rd term = 3 - 3 = 0.

What if I get a negative number as an answer?

That's completely normal! Sequences can have negative terms. In this sequence, the first two terms are actually negative: -2 and -1.

How can I check if my answer is correct?

List out the first few terms to see the pattern:

n = 1: 1 - 3 = -2
n = 2: 2 - 3 = -1
n = 3: 3 - 3 = 0

The pattern should make sense!

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