Complete the Odd Integer Series: Identifying the Missing Numbers in 2n-1

Q: What does the 'n' represent in the formula?

The variable n represents the position of each term in the sequence. So n = 1 gives the first term, n = 2 gives the second term, and so on.

Q: Will this formula always give odd numbers?

Yes! Since $ 2n $ is always even and subtracting 1 from an even number always gives an odd number, this formula generates all positive odd integers.

Q: What if I get confused about which n to use?

Count positions: 1st term, 2nd term, 3rd term...Match n to position: n = 1 for 1st term, n = 2 for 2nd termSubstitute carefully: Write out $ 2(4) - 1 $ instead of just $ 24 - 1 $

Arithmetic Sequences with Algebraic Formulas

Complete the series for the series. $2n-1$

$1,3,5,_—,_—.$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the missing terms

00:03 Identify the location of the missing terms

00:16 Substitute the desired term's position in the sequence formula and solve

00:21 Always solve multiplication and division before addition and subtraction

00:26 This is the fourth term in the sequence

00:29 Use the same method to find the fifth term

00:33 Substitute the desired term's position in the sequence formula and solve

00:38 Always solve multiplication and division before addition and subtraction

00:45 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 series for the series. $2n-1$

$1,3,5,_—,_—.$

Step-by-step solution

To solve this problem, let's analyze the sequence defined by $2n - 1$ , which produces a series of odd numbers. We can identify each term as follows:

First term ( $n = 1$ ): $2 \times 1 - 1 = 1$
Second term ( $n = 2$ ): $2 \times 2 - 1 = 3$
Third term ( $n = 3$ ): $2 \times 3 - 1 = 5$
Fourth term ( $n = 4$ ): $2 \times 4 - 1 = 7$
Fifth term ( $n = 5$ ): $2 \times 5 - 1 = 9$

Therefore, the two missing numbers in the sequence after 5 are 7 and 9, following the pattern of odd numbers.

The series is thus completed to be: $1, 3, 5, 7, 9$ .

In examining the given choices, the correct answer is $7, 9$ .

Final Answer

7,9

Key Points to Remember

Essential concepts to master this topic

Formula Pattern: Each term follows $2n - 1$ where n is position number
Substitution Method: For n = 4: $2(4) - 1 = 7$
Pattern Check: Verify consecutive odd numbers: 1, 3, 5, 7, 9 ✓

Common Mistakes

Avoid these frequent errors

Adding 2 to get the next term
Don't just add 2 to continue the pattern = wrong sequence! This ignores the algebraic formula completely. Always substitute the position number n into $2n - 1$ to find each term.

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

Why can't I just add 2 to each term?

While adding 2 works for this sequence, the problem specifically asks you to use the formula $2n - 1$ . Learning to use formulas prepares you for more complex sequences where simple addition won't work!

What does the 'n' represent in the formula?

The variable n represents the position of each term in the sequence. So n = 1 gives the first term, n = 2 gives the second term, and so on.

How do I know which positions are missing?

Count the given terms: 1 (position 1), 3 (position 2), 5 (position 3). The blanks are positions 4 and 5, so substitute n = 4 and n = 5 into the formula.

Will this formula always give odd numbers?

Yes! Since $2n$ is always even and subtracting 1 from an even number always gives an odd number, this formula generates all positive odd integers.

What if I get confused about which n to use?

Count positions: 1st term, 2nd term, 3rd term...
Match n to position: n = 1 for 1st term, n = 2 for 2nd term
Substitute carefully: Write out $2(4) - 1$ instead of just $24 - 1$

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