Complete the Sequence: Finding the Next Term After 1113, 1112, 1111

Q: How do I know this is an arithmetic sequence and not something else?

Check if the difference between consecutive terms is constant. Here: 1112 - 1113 = -1, and 1111 - 1112 = -1. Since the difference is always -1, it's arithmetic!

Q: What if the numbers looked more complicated, like 2847, 2846, 2845?

The same rule applies! Look for the common difference between consecutive terms. If each term decreases by the same amount, continue that pattern regardless of how big the numbers are.

Q: Could this sequence have a different pattern that I'm missing?

While other patterns are theoretically possible, arithmetic sequences are the most common in these problems. Always try the simplest explanation first - if consecutive differences are equal, you've found your answer!

Q: How many terms ahead should I calculate to be sure?

For this type of problem, calculating 2-3 terms ahead is usually enough to confirm the pattern. The key is showing you understand the rule, not computing many terms.

Q: What if I got confused by the comma notation in the numbers?

The commas are just thousands separators - treat $1{,}113$ as 1113, $1{,}112$ as 1112, etc. Focus on the numerical pattern, not the formatting!

Arithmetic Sequences with Integer Decreasing Pattern

Complete the sequence:

$1{,}113,\ 1{,}112,\ 1{,}111, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$1{,}113,\ 1{,}112,\ 1{,}111, \ \ldots$

Step-by-step solution

The given sequence is $1113, 1112, 1111$ .

Let's analyze the sequence:

The first term is $1113$ .
The second term is $1112$ , which is $1113 - 1$ .
The third term is $1111$ , which is $1112 - 1$ .

It's evident that each term is decreasing by $1$ from the previous term. Therefore, this sequence is an arithmetic sequence with a common difference of $-1$ .

Given this information, we can continue the sequence by subtracting 1 from the last given term, $1111$ .

The next term is $1111 - 1 = 1110$ .
Following that, $1110 - 1 = 1109$ .
Finally, $1109 - 1 = 1108$ .

Thus, the next three terms in the sequence are $1110, 1109,$ and $1108$ .

Looking at the provided options, choice 4: $1110, 1109, 1108$ , is the correct continuation of the sequence.

Final Answer

$1{,}110,\ 1{,}109,\ 1{,}108$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Each term decreases by exactly 1 from the previous term
Common Difference: Calculate d = 1112 - 1113 = -1 throughout the sequence
Verification: Check that 1111 - 1 = 1110, then 1110 - 1 = 1109, then 1109 - 1 = 1108 ✓

Common Mistakes

Avoid these frequent errors

Looking for complex patterns instead of simple arithmetic progression
Don't overthink by looking for multiplication, division, or digit manipulation patterns = missing the obvious decreasing by 1! Students often expect complicated rules when the pattern is straightforward subtraction. Always check if consecutive terms have a constant difference first.

Practice Quiz

Test your knowledge with interactive questions

Complete the sequence:

$1{,}113,\ 1{,}112,\ 1{,}111, \ \ldots$

FAQ

Everything you need to know about this question

How do I know this is an arithmetic sequence and not something else?

Check if the difference between consecutive terms is constant. Here: 1112 - 1113 = -1, and 1111 - 1112 = -1. Since the difference is always -1, it's arithmetic!

What if the numbers looked more complicated, like 2847, 2846, 2845?

The same rule applies! Look for the common difference between consecutive terms. If each term decreases by the same amount, continue that pattern regardless of how big the numbers are.

Could this sequence have a different pattern that I'm missing?

While other patterns are theoretically possible, arithmetic sequences are the most common in these problems. Always try the simplest explanation first - if consecutive differences are equal, you've found your answer!

How many terms ahead should I calculate to be sure?

For this type of problem, calculating 2-3 terms ahead is usually enough to confirm the pattern. The key is showing you understand the rule, not computing many terms.

What if I got confused by the comma notation in the numbers?

The commas are just thousands separators - treat $1{,}113$ as 1113, $1{,}112$ as 1112, etc. Focus on the numerical pattern, not the formatting!

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Complete the Sequence: Finding the Next Term After 1113, 1112, 1111

Arithmetic Sequences with Integer Decreasing Pattern

❤️ Continue Your Math Journey!

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I know this is an arithmetic sequence and not something else?

What if the numbers looked more complicated, like 2847, 2846, 2845?

Could this sequence have a different pattern that I'm missing?

How many terms ahead should I calculate to be sure?

What if I got confused by the comma notation in the numbers?

🌟 Unlock Your Math Potential

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