Complete the Sequence Using Formula 2n-1: Finding Missing Terms

Q: How do I know which n-values to use for the blanks?

Start with the given terms and work backwards! Since 5 comes from $ n=3 $, the blanks before it need $ n=4 $ and $ n=5 $.

Q: Why is the sequence going from big to small numbers?

The sequence itself follows the formula $ 2n-1 $, but it's presented in reverse order. The natural sequence 1, 3, 5, 7, 9 is shown as 9, 7, 5, 3, 1.

Q: What if I calculated 2n-1 = 3 and got n = 1?

That's incorrect! For $ 2n-1 = 3 $: add 1 to both sides to get $ 2n = 4 $, then divide by 2 to get n = 2.

Q: How can I double-check my answer?

Substitute your n-values back into $ 2n-1 $! For $ n=5: 2(5)-1 = 9 $ and for $ n=4: 2(4)-1 = 7 $. Both should match your missing terms.

Q: Is there a pattern I can use instead of the formula?

Yes! This sequence decreases by 2 each time. Starting from 5, count backwards: 5-2=3, 3-2=1. Going forward: 5+2=7, 7+2=9.

Arithmetic Sequences with Formula Applications

Complete the sequence according to the rule $2n-1$ .

._ , _ , 5 , 3 , 1

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the sequence

00:06 Find the appropriate element positions

00:12 Substitute the element position in the sequence formula to find the element

00:16 Substitute N = 4 in the sequence formula

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

00:31 This is the fourth element in the sequence

00:41 We'll use the same method to find the fifth element in the sequence

00:47 Substitute N = 4 in the sequence formula

00:56 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

Complete the sequence according to the rule $2n-1$ .

._ , _ , 5 , 3 , 1

Step-by-step solution

To solve the problem of completing the sequence using the rule $2n - 1$ , follow these steps:

Step 1: Recognize that each term in the sequence is represented by the formula $2n - 1$ . The provided sequence is in reverse order: 5, 3, 1.
Step 2: Identify the value of $n$ that results in each of these terms.
- For term 5: $2n - 1 = 5$ implies $2n = 6$ , thus $n = 3$ .
- For term 3: $2n - 1 = 3$ implies $2n = 4$ , thus $n = 2$ .
- For term 1: $2n - 1 = 1$ implies $2n = 2$ , thus $n = 1$ .
Step 3: Consider the terms preceding the known sequence, calculating them for $n = 4$ and $n = 5$ :
- For $n = 4$ , $2n - 1 = 2 \cdot 4 - 1 = 7$ .
- For $n = 5$ , $2n - 1 = 2 \cdot 5 - 1 = 9$ .
Step 4: Identify the missing numbers to complete the sequence: 9 and 7 must be placed before the given sequence 5, 3, 1.

Therefore, the completed sequence, according to the rule $2n - 1$ , is 9, 7, 5, 3, 1.

Final Answer

9 , 7

Key Points to Remember

Essential concepts to master this topic

Pattern Rule: Use formula $2n-1$ to find any term position
Technique: Work backwards from known terms: if $2n-1 = 5$ , then $n = 3$
Check: Verify sequence follows pattern: 9, 7, 5, 3, 1 decreases by 2 each time ✓

Common Mistakes

Avoid these frequent errors

Confusing sequence position with term value
Don't assume the first blank needs n=1 because it's first position = wrong sequence order! The sequence goes backwards, so you need n=5 and n=4 for the missing terms. Always identify which n-values produce the given terms first.

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

How do I know which n-values to use for the blanks?

Start with the given terms and work backwards! Since 5 comes from $n=3$ , the blanks before it need $n=4$ and $n=5$ .

Why is the sequence going from big to small numbers?

The sequence itself follows the formula $2n-1$ , but it's presented in reverse order. The natural sequence 1, 3, 5, 7, 9 is shown as 9, 7, 5, 3, 1.

What if I calculated 2n-1 = 3 and got n = 1?

That's incorrect! For $2n-1 = 3$ : add 1 to both sides to get $2n = 4$ , then divide by 2 to get n = 2.

How can I double-check my answer?

Substitute your n-values back into $2n-1$ ! For $n=5: 2(5)-1 = 9$ and for $n=4: 2(4)-1 = 7$ . Both should match your missing terms.

Is there a pattern I can use instead of the formula?

Yes! This sequence decreases by 2 each time. Starting from 5, count backwards: 5-2=3, 3-2=1. Going forward: 5+2=7, 7+2=9.

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