Uncover the Decreasing Pattern: 12,000,000, 11,000,000, ...

Q: How do I know if the sequence is increasing or decreasing?

Look at the first two terms! Since $ 12{,}000{,}000 > 11{,}000{,}000 $, the sequence is decreasing. Each term gets smaller by the same amount.

Q: How many terms should I find in the sequence?

Usually the problem tells you! Look for phrases like "find the next three terms" or count how many blanks need to be filled in the answer choices.

Q: Can arithmetic sequences have negative numbers?

Absolutely! If this sequence continued long enough, you'd eventually get to 0, then -1,000,000, -2,000,000, etc. The pattern stays the same!

Q: What's the fastest way to find the 10th term?

Use the formula: nth term = first term + (n-1) × common difference. For the 10th term: $ 12{,}000{,}000 + (10-1) × (-1{,}000{,}000) = 3{,}000{,}000 $.

Arithmetic Sequences with Million-Unit Decreases

Complete the sequence:

$12{,}000{,}000,\ 11{,}000{,}000, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$12{,}000{,}000,\ 11{,}000{,}000, \ \ldots$

Step-by-step solution

To solve this problem, we need to determine the pattern of the given number sequence:

Step 1: Identify the pattern in the sequence. The sequence begins with $12{,}000{,}000$ followed by $11{,}000{,}000$ .
Step 2: Calculate the difference between the two given terms. The difference is $12{,}000{,}000 - 11{,}000{,}000 = 1{,}000{,}000$ .
Step 3: This indicates a consistent decrease by $1{,}000{,}000$ between consecutive terms.
Step 4: To find the next number after $11{,}000{,}000$ , subtract $1{,}000{,}000$ , yielding $10{,}000{,}000$ .
Step 5: Continue applying this pattern:
- The number after $10{,}000{,}000$ is $10{,}000{,}000 - 1{,}000{,}000 = 9{,}000{,}000$ .
- Finally, the number after $9{,}000{,}000$ is $9{,}000{,}000 - 1{,}000{,}000 = 8{,}000{,}000$ .

Hence, the next numbers in the sequence are $10{,}000{,}000$ , $9{,}000{,}000$ , and $8{,}000{,}000$ .

Therefore, the correct continuation of the sequence is $10{,}000{,}000,\ 9{,}000{,}000,\ 8{,}000{,}000$ .

Final Answer

$10{,}000{,}000,\ 9{,}000{,}000, \ 8{,}000{,}000$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Each term decreases by exactly one million
Technique: Calculate difference: $12{,}000{,}000 - 11{,}000{,}000 = 1{,}000{,}000$
Check: Verify pattern holds for all terms: consistent $-1{,}000{,}000$ difference ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting the common difference
Don't add 1,000,000 to continue the pattern = 12,000,000, 13,000,000! This creates an increasing sequence when the numbers are clearly getting smaller. Always identify whether the sequence increases or decreases first, then apply the correct operation.

Practice Quiz

Test your knowledge with interactive questions

Complete the sequence:

$20{,}000,\ 20{,}001,\ 20{,}002, \ \ldots$

FAQ

Everything you need to know about this question

How do I know if the sequence is increasing or decreasing?

Look at the first two terms! Since $12{,}000{,}000 > 11{,}000{,}000$ , the sequence is decreasing. Each term gets smaller by the same amount.

What if the numbers don't decrease by round millions?

The same method works! Find the difference between consecutive terms. For example, if you had 12,500,000 then 11,200,000, the difference would be 1,300,000.

How many terms should I find in the sequence?

Usually the problem tells you! Look for phrases like "find the next three terms" or count how many blanks need to be filled in the answer choices.

Can arithmetic sequences have negative numbers?

Absolutely! If this sequence continued long enough, you'd eventually get to 0, then -1,000,000, -2,000,000, etc. The pattern stays the same!

What's the fastest way to find the 10th term?

Use the formula: nth term = first term + (n-1) × common difference. For the 10th term: $12{,}000{,}000 + (10-1) × (-1{,}000{,}000) = 3{,}000{,}000$ .

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