Find the Third Term in a Sequence with Rule n/2

Q: What does n represent in the sequence formula?

n represents the position of the term in the sequence. For the third term, n = 3. For the fifth term, n = 5, and so on.

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

Simply substitute the position number for n in the formula $ \frac{n}{2} $. Want the 10th term? Use n = 10 to get $ \frac{10}{2} = 5 $.

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

The sequence rule $ \frac{n}{2} $ means you divide the position by 2. So the third term = $ \frac{3}{2} $, not 3.

Q: What would the first few terms of this sequence be?

1st term: $ \frac{1}{2} $2nd term: $ \frac{2}{2} = 1 $3rd term: $ \frac{3}{2} $4th term: $ \frac{4}{2} = 2 $

Q: Can I check my answer by looking at the pattern?

Absolutely! The terms increase by $ \frac{1}{2} $ each time: $ \frac{1}{2}, 1, \frac{3}{2}, 2... $ This confirms the third term is $ \frac{3}{2} $.

Sequence Terms with Position Substitution

A sequence has the following term-to-term rule:

$\frac{n}{2}$

What is the the third term?

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Step-by-step video solution

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00:00 Find the 3rd term

00:03 Substitute the desired term's position in the sequence formula and solve

00:19 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

A sequence has the following term-to-term rule:

$\frac{n}{2}$

What is the the third term?

Step-by-step solution

The third term in the sequence is the term $a_3$ :

$a_n= \frac{n}{2}$

We need to substitute in the position of the term in the sequence:

$n=3$

Now, using our values:

$a_{\underline{n}}= \frac{\underline{n}}{2} \\ n=\underline{3}\\ \downarrow\\ a_{\underline{3}}=\frac{\underline{3}}{2}$

Now we substitute the position of the term in the sequence (3) in place of n. The substitution is shown with an underline in the expression above.

Therefore, the correct answer is answer C.

Final Answer

$\frac{3}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Position number n substitutes into the given formula
Technique: For third term, substitute n = 3 into $\frac{n}{2}$ = $\frac{3}{2}$
Check: Position 3 gives $\frac{3}{2}$ , position 1 gives $\frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Using the term value instead of position number
Don't substitute the term's value for n = wrong formula usage! This confuses what n represents in the sequence rule. Always substitute the position number (1st, 2nd, 3rd, etc.) for n in the formula.

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 sequence formula?

n represents the position of the term in the sequence. For the third term, n = 3. For the fifth term, n = 5, and so on.

How do I find any term in this sequence?

Simply substitute the position number for n in the formula $\frac{n}{2}$ . Want the 10th term? Use n = 10 to get $\frac{10}{2} = 5$ .

Why isn't the third term equal to 3?

The sequence rule $\frac{n}{2}$ means you divide the position by 2. So the third term = $\frac{3}{2}$ , not 3.

What would the first few terms of this sequence be?

1st term: $\frac{1}{2}$
2nd term: $\frac{2}{2} = 1$
3rd term: $\frac{3}{2}$
4th term: $\frac{4}{2} = 2$

Can I check my answer by looking at the pattern?

Absolutely! The terms increase by $\frac{1}{2}$ each time: $\frac{1}{2}, 1, \frac{3}{2}, 2...$ This confirms the third term is $\frac{3}{2}$ .

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