Complete the Decimal Sequence: Finding Missing Terms in 0.1, 0.09, ..., 0.05

Arithmetic Sequences with Decimal Differences

Complete the following sequence:

0.1,0.09,?,?,0.06,0.05 0.1,0.09,?,?,0.06,0.05

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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 Subtract between the numbers to find the difference
00:55 This is the difference between term and term
01:05 We'll use this pattern and add the difference to find the next term
01:38 This is the next term, we'll use the same method for the remaining terms
02:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the following sequence:

0.1,0.09,?,?,0.06,0.05 0.1,0.09,?,?,0.06,0.05

2

Step-by-step solution

The sequence provided is 0.1,0.09,?,?,0.06,0.050.1, 0.09, ?, ?, 0.06, 0.05.

First, observe the difference between the first two numbers of the sequence:

0.10.09=0.010.1 - 0.09 = 0.01.

This indicates that the sequence decreases by 0.010.01 between consecutive terms.

Apply this pattern to find the missing numbers:

1. From 0.090.09, subtract 0.010.01 to find the next term:
0.090.01=0.08 0.09 - 0.01 = 0.08 .

2. From 0.080.08, again subtract 0.010.01:
0.080.01=0.07 0.08 - 0.01 = 0.07 .

This reveals the sequence as:

0.1,0.09,0.08,0.07,0.06,0.050.1, 0.09, 0.08, 0.07, 0.06, 0.05.

Therefore, the missing terms in the sequence are 0.080.08 and 0.070.07.

The correct answer, matching the choice is 0.08,0.070.08, 0.07.

3

Final Answer

0.08,0.07 0.08,0.07

Key Points to Remember

Essential concepts to master this topic
  • Pattern Recognition: Find the common difference between consecutive terms first
  • Technique: Calculate 0.10.09=0.01 0.1 - 0.09 = 0.01 , then subtract repeatedly
  • Check: Verify pattern continues: 0.070.06=0.01 0.07 - 0.06 = 0.01

Common Mistakes

Avoid these frequent errors
  • Assuming the pattern without calculating the difference
    Don't guess the pattern by looking at just two numbers = wrong sequence! You might think it decreases by 0.1 or some other amount. Always calculate the exact difference between consecutive terms first.

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 what the common difference is?

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Subtract the second term from the first term: 0.10.09=0.01 0.1 - 0.09 = 0.01 . This tells you the sequence decreases by 0.01 each time.

What if the difference is negative?

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That's normal! A negative difference means the sequence is decreasing. In our case, we subtract 0.01 each time, so we're going down: 0.1 → 0.09 → 0.08 → 0.07...

Can I check my answer using the given terms?

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Absolutely! Use the terms 0.06 and 0.05 to verify. If 0.07 → 0.06 has the same difference (0.01), and 0.06 → 0.05 also differs by 0.01, you're correct!

What if I get confused with decimal subtraction?

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Line up the decimal points carefully! For 0.090.01 0.09 - 0.01 , write it as:

  • 0.09
  • - 0.01
  • = 0.08

How many terms should I calculate?

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Calculate exactly what's asked! This problem has two missing terms, so find the 3rd and 4th terms: 0.08 and 0.07.

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