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

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

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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