Complete the Decimal Sequence: Finding Missing Terms in 0, 0.01, 0.02, ?, ?

Q: How do I know if a sequence is arithmetic?

Check if the difference between consecutive terms is constant. In this sequence: 0.01 - 0 = 0.01 and 0.02 - 0.01 = 0.01, so it's arithmetic with common difference 0.01.

Q: What if I get confused with decimal places?

Line up the decimal points when adding! Write $ 0.02 + 0.01 $ as:0.02+ 0.01______0.03This keeps decimal places aligned correctly.

Q: Can arithmetic sequences have negative common differences?

Yes! If each term gets smaller by the same amount, the common difference is negative. For example: 0.05, 0.04, 0.03... has common difference -0.01.

Q: What if the differences aren't exactly equal?

Then it's not an arithmetic sequence. Double-check your calculations. If differences are close but not identical, the sequence might follow a different pattern or contain rounding errors.

Arithmetic Sequences with Decimal Increments

Complete the following sequence:

$0,0.01,0.02,?,\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's complete the sequence.

00:14 First, subtract the numbers to find the difference between each pair.

00:35 This is how we determine the difference between terms.

00:55 Now, use this pattern. Add the difference to find the next term.

01:08 Here's the next term! We'll repeat this method for the rest.

01:45 And there you have it! That's how we solve the question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following sequence:

$0,0.01,0.02,?,\text{?}$

Step-by-step solution

To complete the sequence, let's observe the given numbers: $0, 0.01, 0.02$ .

Step 1: Calculate the difference between the consecutive terms:

Difference between $0$ and $0.01$ : $0.01 - 0 = 0.01$ .
Difference between $0.01$ and $0.02$ : $0.02 - 0.01 = 0.01$ .

Step 2: The difference between each term is $0.01$ , suggesting a pattern where each term increases by $0.01$ .

Step 3: Apply this pattern to find the next terms:

The term after $0.02$ is $0.02 + 0.01 = 0.03$ .
The term after $0.03$ is $0.03 + 0.01 = 0.04$ .

Therefore, the completed sequence is $0, 0.01, 0.02, 0.03, 0.04$ .

Comparing this with the choices provided, the correct choice is:

$0.03,0.04$

Final Answer

$0.03,0.04$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference between consecutive terms
Technique: Add 0.01 repeatedly: 0.02 + 0.01 = 0.03, then 0.03 + 0.01 = 0.04
Check: Verify each difference equals 0.01: 0.04 - 0.03 = 0.01 ✓

Common Mistakes

Avoid these frequent errors

Confusing decimal place values when finding patterns
Don't assume 0.02 + 0.1 = 0.3 just because 2 + 1 = 3! This ignores decimal place value and gives 0.3 instead of 0.03. Always keep track of decimal places and add the exact common difference found between the first terms.

Practice Quiz

Test your knowledge with interactive questions

Determine the numerical value of the shaded area:

FAQ

Everything you need to know about this question

How do I know if a sequence is arithmetic?

Check if the difference between consecutive terms is constant. In this sequence: 0.01 - 0 = 0.01 and 0.02 - 0.01 = 0.01, so it's arithmetic with common difference 0.01.

What if I get confused with decimal places?

Line up the decimal points when adding! Write $0.02 + 0.01$ as:
0.02
+ 0.01
______
0.03
This keeps decimal places aligned correctly.

Can arithmetic sequences have negative common differences?

Yes! If each term gets smaller by the same amount, the common difference is negative. For example: 0.05, 0.04, 0.03... has common difference -0.01.

How many terms ahead can I predict?

As many as you want! Once you know the pattern, use the formula: next term = current term + common difference. You can find the 10th term, 100th term, or any term in the sequence.

What if the differences aren't exactly equal?

Then it's not an arithmetic sequence. Double-check your calculations. If differences are close but not identical, the sequence might follow a different pattern or contain rounding errors.

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