Evaluate 2(2n-2): Finding the Position of 20 in the Sequence

Q: What does it mean for a number to be 'part of the sequence'?

A number is part of the sequence if you can find a positive integer value of n that makes the formula equal that number. If n isn't a positive integer, the number doesn't appear in the sequence.

Q: Why do we need n to be positive?

Sequence positions start at n = 1, 2, 3... because you can't have a 0th term or negative position! If you get n = 0 or negative, that number isn't in the sequence.

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

If n is not a whole number, then that target value doesn't appear in the sequence. Positions must be counting numbers: 1st term, 2nd term, 3rd term, etc.

Q: How do I solve 2(2n-2) = 20 step by step?

Step 1: Distribute: $ 4n - 4 = 20 $Step 2: Add 4: $ 4n = 24 $Step 3: Divide by 4: $ n = 6 $

Q: Should I always check my answer?

Absolutely! Substitute your n-value back into the original formula. If you get the target number, you're correct. For this problem: $ 2(2 \cdot 6 - 2) = 2(10) = 20 $ ✓

Sequence Formulas with Position Finding

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

$2(2n-2)$

Is the number 20 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

00:11 Is the number 20 part of our sequence, and if it is, what position does it hold?

00:17 To find out, let's insert 20 into the sequence formula and see what happens.

00:22 If our answer for N is both positive and a whole number, that means 20 is a term and N is its position.

00:29 Let's simplify the equation as much as we can.

00:33 Next, we'll isolate the variable N in our equation.

00:50 And that's how we figure out if 20 is in the sequence!

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 $n$ :

$2(2n-2)$

Is the number 20 Is it part of the series? If so, what element is it in the series?

Step-by-step solution

To determine if the number 20 is part of the sequence given by the formula $2(2n-2)$ , we proceed as follows:

Step 1: Set up the equation, $2(2n-2) = 20$ .
Step 2: Simplify the equation:
$2(2n-2) = 4n - 4$ , thus we have $4n - 4 = 20$ .
Step 3: Solve for $n$ :
Add 4 to both sides: $4n - 4 + 4 = 20 + 4$ gives $4n = 24$ .
Divide both sides by 4: $n = \frac{24}{4} = 6$ .
Step 4: Check if $n$ is a positive integer.
$n = 6$ is indeed a positive integer.

Since $n = 6$ is a positive integer, 20 is indeed part of the sequence, and it is the 6th term.

Therefore, the solution to the problem is Yes, 6.

Final Answer

Yes, $6$

Key Points to Remember

Essential concepts to master this topic

Formula Setup: Set expression equal to given value to find position
Algebraic Solution: Solve $2(2n-2) = 20$ gives $n = 6$
Verification: Substitute back: $2(2 \cdot 6 - 2) = 2(10) = 20$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to check if n is a positive integer
Don't assume any solution works in sequences = wrong position identification! Sequences only use positive whole numbers for positions. Always verify that your calculated n-value is a positive integer before concluding the term exists.

Practice Quiz

Test your knowledge with interactive questions

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

FAQ

Everything you need to know about this question

What does it mean for a number to be 'part of the sequence'?

A number is part of the sequence if you can find a positive integer value of n that makes the formula equal that number. If n isn't a positive integer, the number doesn't appear in the sequence.

Why do we need n to be positive?

Sequence positions start at n = 1, 2, 3... because you can't have a 0th term or negative position! If you get n = 0 or negative, that number isn't in the sequence.

What if I get a decimal or fraction for n?

If n is not a whole number, then that target value doesn't appear in the sequence. Positions must be counting numbers: 1st term, 2nd term, 3rd term, etc.

How do I solve 2(2n-2) = 20 step by step?

Step 1: Distribute: $4n - 4 = 20$
Step 2: Add 4: $4n = 24$
Step 3: Divide by 4: $n = 6$

Should I always check my answer?

Absolutely! Substitute your n-value back into the original formula. If you get the target number, you're correct. For this problem: $2(2 \cdot 6 - 2) = 2(10) = 20$ ✓

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