Complete the Sequence: Finding Missing Terms Around 8500

Q: How do I know the sequence increases by 1?

When no specific pattern is given, consecutive integers are the standard assumption. This means each number is exactly 1 more than the previous number.

Q: What if the sequence had a different pattern?

The problem would provide more information like additional numbers or a rule. For example: "increases by 10" or showing more terms like 8490, 8500, ___.

Q: Why not 8499 and 8510 as the answer?

That would create an inconsistent pattern: 8499 → 8500 (+1), then 8500 → 8510 (+10). Sequences need consistent differences between terms.

Q: What's the difference between predecessor and successor?

Predecessor: The number that comes before (subtract 1)Successor: The number that comes after (add 1)For 8500: predecessor is 8499, successor is 8501.

Number Sequences with Consecutive Integers

Fill in the missing numbers:

$\Box,8500,\Box$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing numbers:

$\Box,8500,\Box$

Step-by-step solution

Let's solve the problem following these steps:

Step 1: Identify the given information: We have a number 8500 and an indication of a sequence: $\Box, 8500, \Box$ .
Step 2: Find the predecessor: Using the formula for the predecessor of a number, calculate $8500 - 1 = 8499$ .
Step 3: Find the successor: Using the formula for the successor of a number, calculate $8500 + 1 = 8501$ .

By computing these values, we find the missing numbers in the sequence as 8499 and 8501. Therefore, the sequence is: $8499, 8500, 8501$ .

The correct choice from the provided multiple-choice answers is: $8499,8501$ .

Final Answer

$8499,8501$

Key Points to Remember

Essential concepts to master this topic

Consecutive Rule: Each number in sequence differs by exactly 1
Technique: Subtract 1 for predecessor: $8500 - 1 = 8499$
Check: Verify sequence increases by 1: 8499, 8500, 8501 ✓

Common Mistakes

Avoid these frequent errors

Assuming sequences have different patterns
Don't add or subtract random amounts like 10, 100, or 99 = wrong sequence! Without clear pattern information, consecutive integers (±1) is the standard. Always use predecessor (n-1) and successor (n+1) for basic sequences.

Practice Quiz

Test your knowledge with interactive questions

Select the predecessor of the number 2100:

FAQ

Everything you need to know about this question

How do I know the sequence increases by 1?

When no specific pattern is given, consecutive integers are the standard assumption. This means each number is exactly 1 more than the previous number.

What if the sequence had a different pattern?

The problem would provide more information like additional numbers or a rule. For example: "increases by 10" or showing more terms like 8490, 8500, ___.

Why not 8499 and 8510 as the answer?

That would create an inconsistent pattern: 8499 → 8500 (+1), then 8500 → 8510 (+10). Sequences need consistent differences between terms.

What's the difference between predecessor and successor?

Predecessor: The number that comes before (subtract 1)
Successor: The number that comes after (add 1)

For 8500: predecessor is 8499, successor is 8501.

Can sequences go backwards?

Yes! If the pattern decreases, like 8502, 8501, 8500, then the next would be 8499. Always look at the direction and amount of change.

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