Is 30 a Term in the Sequence Defined by 6n?

Q: What if I get a decimal or fraction when solving for n?

If n is not a positive whole number, then the given number is not a term in the sequence! Sequence positions must be positive integers like 1, 2, 3, etc.

Q: How do I know which term position a number represents?

Set up the equation: sequence rule = given number. For 6n = 30, solve to get n = 5, so 30 is the 5th term, not the 30th!

Q: What's the difference between the term value and term position?

Term position is where the term appears in the sequence (1st, 2nd, 3rd, etc.). Term value is the actual number at that position. Here, position 5 has value 30.

Sequence Terms with Position Finding

A sequence has a rule of $6n$ .

Is the number 30 a term in the sequence?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Is the number thirty a part of the sequence?

00:10 Let's put the number into the sequence formula and find N.

00:15 If N is a positive whole number, that's its spot in the sequence.

00:20 Now, we'll solve for N carefully.

00:31 And that's how we find the answer. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A sequence has a rule of $6n$ .

Is the number 30 a term in the sequence?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Use the sequence rule to form the equation $6n = 30$ .
Step 2: Solve the equation for $n$ .
Step 3: Determine if the solution is a positive integer and identify the term position.

Now, let's work through each step:
Step 1: Set up the equation using the rule of the sequence: $6n = 30$ .
Step 2: Solve for $n$ by dividing both sides by 6:
$n = \frac{30}{6} = 5$ .
Step 3: Since $n = 5$ is a positive integer, 30 is a term in the sequence, specifically the fifth term.

Therefore, the solution to the problem is Yes, it is the fifth term.

Final Answer

Yes, it is the fifth term.

Key Points to Remember

Essential concepts to master this topic

Rule: Set sequence formula equal to given value to find position
Technique: Solve $6n = 30$ by dividing: n = 5
Check: Substitute back: 6(5) = 30, so 30 is the 5th term ✓

Common Mistakes

Avoid these frequent errors

Assuming the term position equals the term value
Don't think that 30 is the 30th term just because it's the number you're looking for = wrong position! This ignores the sequence rule completely. Always solve the equation 6n = 30 to find the actual position.

Practice Quiz

Test your knowledge with interactive questions

Look at the following set of numbers and determine if there is any property, if so, what is it?

$$ 94,96,98,100,102,104 $$

FAQ

Everything you need to know about this question

What if I get a decimal or fraction when solving for n?

If n is not a positive whole number, then the given number is not a term in the sequence! Sequence positions must be positive integers like 1, 2, 3, etc.

How do I know which term position a number represents?

Set up the equation: sequence rule = given number. For 6n = 30, solve to get n = 5, so 30 is the 5th term, not the 30th!

What's the difference between the term value and term position?

Term position is where the term appears in the sequence (1st, 2nd, 3rd, etc.). Term value is the actual number at that position. Here, position 5 has value 30.

Can I just divide the number by the coefficient to find the position?

Yes! For a sequence rule like 6n, divide the term value by 6. So 30 ÷ 6 = 5, meaning 30 is the 5th term. Always check: 6(5) = 30 ✓

What if the sequence rule is more complicated than 6n?

The same method works! Set the rule equal to your number and solve for n. For example, if the rule is $3n + 2$ , solve $3n + 2 = 30$ to find the position.

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