Find the Eighth Term in the n/2 Sequence Formula

Q: What does n represent in the sequence formula?

The variable n represents the position of the term in the sequence. For the 1st term, n = 1; for the 8th term, n = 8. It's like the term's address in the sequence!

Q: Why isn't the answer 8 since we want the eighth term?

The position is 8, but the value at that position is different! We substitute n = 8 into $ \frac{n}{2} $ to get $ \frac{8}{2} = 4 $. Think of it like house addresses - house #8 might have 4 people living in it!

Q: Can sequence formulas give decimal or fraction answers?

Absolutely! Sequences can have any type of numbers - whole numbers, fractions, decimals, even negative numbers. The formula $ \frac{n}{2} $ gives us fractions when n is odd and whole numbers when n is even.

Sequence Formulas with Term Position Substitution

What is the eighth element of the sequence below?

$\frac{n}{2}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the 8th element in the sequence

00:03 Let's substitute the position of the corresponding element in the sequence formula and solve

00:08 Let's substitute N = 8 in the sequence formula

00:15 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the eighth element of the sequence below?

$\frac{n}{2}$

Step-by-step solution

To find the eighth element of the sequence defined by the formula $\frac{n}{2}$ , we will follow these steps:

Identify the formula provided for the sequence: $a_n = \frac{n}{2}$ .
Determine the position in the sequence we need: $n = 8$ .
Substitute $n = 8$ into the formula to find $a_8$ .

Substituting $n = 8$ into the formula, we have:

$a_8 = \frac{8}{2}$ .

This simplifies to $a_8 = 4$ .

Therefore, the eighth element of the sequence is $4$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula Rule: Substitute term position n directly into sequence formula
Technique: Replace n with 8 in $\frac{n}{2}$ to get $\frac{8}{2} = 4$
Check: Verify that position 8 gives $a_8 = 4$ by computing $\frac{8}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Using the formula value instead of position number
Don't substitute the answer 4 back into the formula = circular reasoning! This doesn't tell you which term you found. Always substitute the position number (n = 8) into the given formula $\frac{n}{2}$ .

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?

The variable n represents the position of the term in the sequence. For the 1st term, n = 1; for the 8th term, n = 8. It's like the term's address in the sequence!

How do I know which number to substitute for n?

Look at what the question is asking for! If it asks for the eighth element, then n = 8. If it asked for the 5th term, then n = 5. The position number always equals n.

Why isn't the answer 8 since we want the eighth term?

The position is 8, but the value at that position is different! We substitute n = 8 into $\frac{n}{2}$ to get $\frac{8}{2} = 4$ . Think of it like house addresses - house #8 might have 4 people living in it!

What would the first few terms of this sequence look like?

Let's see:

1st term (n=1): $\frac{1}{2} = 0.5$
2nd term (n=2): $\frac{2}{2} = 1$
3rd term (n=3): $\frac{3}{2} = 1.5$

The sequence is: 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, ...

Can sequence formulas give decimal or fraction answers?

Absolutely! Sequences can have any type of numbers - whole numbers, fractions, decimals, even negative numbers. The formula $\frac{n}{2}$ gives us fractions when n is odd and whole numbers when n is even.

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