Identify Even-Numbered Terms: Sequence Using 4n-3 to the Eighth Term

Q: What does 'even-numbered positions' mean exactly?

Even-numbered positions refer to the placement of terms in the sequence: 2nd, 4th, 6th, 8th, etc. Don't confuse this with whether the term values are even numbers!

Q: How do I remember which positions to use?

Think of it like seat numbers in a theater. Even positions are seats 2, 4, 6, 8... These are the values you substitute for n in your formula.

Q: Why isn't the first term included?

Position 1 is an odd position, not even! We only want terms at positions 2, 4, 6, and 8 when looking for even-numbered places.

Q: Can I calculate all 8 terms first then pick the even ones?

Yes, that works too! Calculate $ a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8 $ then select the 2nd, 4th, 6th, and 8th values. Both methods give the same answer.

Q: What if I get the wrong final answer?

Double-check your arithmetic and make sure you used n = 2, 4, 6, 8 (not 1, 3, 5, 7). Recalculate each term step-by-step: multiply first, then subtract 3.

Sequence Terms with Even Position Indices

Which terms occupy the even-numbered places up until the eighth term of the sequence below? $4n-3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find all even terms up to term 8

00:06 Let's start by identifying all even terms

00:12 We'll substitute the desired term position in the sequence formula and solve

00:28 Always solve multiplication and division before addition and subtraction

00:35 This is the first even term in the sequence

00:41 We'll use the same method to find the next terms

00:46 We'll substitute the desired term position in the sequence formula and solve

00:59 This is the second even term(4)

01:04 We'll substitute the desired term position in the sequence formula and solve

01:21 This is the third even term(6)

01:32 We'll substitute the desired term position in the sequence formula and solve

01:47 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which terms occupy the even-numbered places up until the eighth term of the sequence below? $4n-3$

Step-by-step solution

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

Step 1: Calculate terms of the sequence for even indices.
Step 2: Select terms corresponding to the 2nd, 4th, 6th, and 8th positions.
Step 3: Verify against multiple-choice options.

Now, let's work through each step:
Step 1: Use the formula $a_n = 4n - 3$ .
- For $n = 2$ , $a_2 = 4(2) - 3 = 8 - 3 = 5$ .
- For $n = 4$ , $a_4 = 4(4) - 3 = 16 - 3 = 13$ .
- For $n = 6$ , $a_6 = 4(6) - 3 = 24 - 3 = 21$ .
- For $n = 8$ , $a_8 = 4(8) - 3 = 32 - 3 = 29$ .

Step 2: The sequence terms at even positions up to the 8th position are 5, 13, 21, and 29.

Step 3: Compare these with the given choices. The option matching our result is choice 4: $5, 13, 21, 29$ .

Therefore, the correct terms occupying the even-numbered places are 5, 13, 21, 29.

Final Answer

5,13,21,29

Key Points to Remember

Essential concepts to master this topic

Formula Application: Substitute even position numbers (2, 4, 6, 8) into $4n-3$
Calculation Method: For position 4: $a_4 = 4(4) - 3 = 13$
Position Check: Even positions are 2nd, 4th, 6th, 8th places only ✓

Common Mistakes

Avoid these frequent errors

Finding terms at odd positions instead of even
Don't substitute n = 1, 3, 5, 7 when asked for even-numbered positions = wrong terms like 1, 9, 17, 25! Even positions means the 2nd, 4th, 6th, 8th places in the sequence. Always use n = 2, 4, 6, 8 for even-numbered positions.

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 'even-numbered positions' mean exactly?

Even-numbered positions refer to the placement of terms in the sequence: 2nd, 4th, 6th, 8th, etc. Don't confuse this with whether the term values are even numbers!

How do I remember which positions to use?

Think of it like seat numbers in a theater. Even positions are seats 2, 4, 6, 8... These are the values you substitute for n in your formula.

Why isn't the first term included?

Position 1 is an odd position, not even! We only want terms at positions 2, 4, 6, and 8 when looking for even-numbered places.

Can I calculate all 8 terms first then pick the even ones?

Yes, that works too! Calculate $a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8$ then select the 2nd, 4th, 6th, and 8th values. Both methods give the same answer.

What if I get the wrong final answer?

Double-check your arithmetic and make sure you used n = 2, 4, 6, 8 (not 1, 3, 5, 7). Recalculate each term step-by-step: multiply first, then subtract 3.

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