Find Position of 9 in Sequence 2n+2: Term Identification Problem

Q: Why can't n be a fraction like 7/2?

In sequences, n represents the position of a term (1st term, 2nd term, etc.). You can't have a half position like the 3.5th term - it doesn't make sense!

Q: How do I check if any number is in this sequence?

Set up the equation $ 2n + 2 = \text{your number} $, solve for n, and check if n is a positive integer. If yes, the number is in the sequence at position n.

Q: What are the first few terms of this sequence?

n = 1: $ 2(1) + 2 = 4 $n = 2: $ 2(2) + 2 = 6 $n = 3: $ 2(3) + 2 = 8 $n = 4: $ 2(4) + 2 = 10 $Notice 9 isn't here - it falls between 8 and 10!

Q: Can sequences skip numbers?

Yes! This sequence $ 2n + 2 $ only produces even numbers (4, 6, 8, 10...), so all odd numbers like 9 are not included.

Sequence Term Identification with Non-Integer Solutions

Given a formula with a constant property that depends on $n$ :

$2n+2$

Is the number 9 Is it part of the series? If so, what element is it in the series?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Is the number 9 in the sequence? If yes, what position is it in?

00:14 Let's put 9 into the sequence formula and solve it together!

00:19 If our answer for N is a positive whole number, then 9 is in the sequence at spot N.

00:25 Now, let's go step-by-step to find N. Ready? Here we go!

00:34 We got a solution for N that is positive, but it's not a whole number.

00:38 So, 9 is not a member of this sequence.

00:42 And that's how we answer this question! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given a formula with a constant property that depends on $n$ :

$2n+2$

Is the number 9 Is it part of the series? If so, what element is it in the series?

Step-by-step solution

To determine if 9 is part of the sequence given by the formula $2n + 2$ , we need to solve the equation for $n$ :

$2n + 2 = 9$

Subtract 2 from both sides:

$2n = 7$

Divide both sides by 2:

$n = \frac{7}{2}$

The solution $n = \frac{7}{2}$ is not an integer, meaning there is no integer $n$ such that $2n + 2 = 9$ . Therefore, the number 9 is not part of the sequence.

In conclusion, the number 9 does not belong in the sequence defined by $2n + 2$ , so the answer is No.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Sequence Rule: Set formula equal to target value and solve
Technique: Solve $2n + 2 = 9$ gives $n = \frac{7}{2}$
Check: If n is not a positive integer, the number isn't in the sequence ✓

Common Mistakes

Avoid these frequent errors

Accepting fractional position values
Don't assume fractional n values like 3.5 are valid positions in a sequence = impossible term location! Sequence positions must be positive integers (1st, 2nd, 3rd, etc.). Always check if your n value is a positive integer before concluding the number exists in the sequence.

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

Why can't n be a fraction like 7/2?

In sequences, n represents the position of a term (1st term, 2nd term, etc.). You can't have a half position like the 3.5th term - it doesn't make sense!

What does it mean when I get a non-integer solution?

When solving gives you a fraction or decimal for n, it means the target number is not part of the sequence. The sequence only produces values at integer positions.

How do I check if any number is in this sequence?

Set up the equation $2n + 2 = \text{your number}$ , solve for n, and check if n is a positive integer. If yes, the number is in the sequence at position n.

What are the first few terms of this sequence?

n = 1: $2(1) + 2 = 4$
n = 2: $2(2) + 2 = 6$
n = 3: $2(3) + 2 = 8$
n = 4: $2(4) + 2 = 10$

Notice 9 isn't here - it falls between 8 and 10!

Can sequences skip numbers?

Yes! This sequence $2n + 2$ only produces even numbers (4, 6, 8, 10...), so all odd numbers like 9 are not included.

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