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

Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

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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