Complete the Sequence: Finding the Pattern in 305,501, 305,500, ...

Q: How do I know if the sequence goes up or down?

Look at the first two terms! If the second number is smaller than the first (like 305,500 decreasing. If it's larger, the sequence is increasing.

Q: What if the difference isn't 1?

The same method works! Just find the difference between any two consecutive terms. For example, if terms decrease by 5 each time, subtract 5 from each previous term.

Q: Do I need to show all the calculations?

Yes! Show each step: find the common difference, then apply it to get each new term. This helps you catch mistakes and shows your thinking clearly.

Q: Can arithmetic sequences have fractions or decimals?

Absolutely! The common difference can be any number - whole numbers, fractions, or decimals. The key is that it stays constant between consecutive terms.

Q: What if I get confused about which direction to go?

Write down what you know first: 305,501 → 305,500. The arrow shows decreasing by 1, so continue: 305,500 → 305,499 → 305,498, and so on.

Arithmetic Sequences with Consecutive Integer Differences

Complete the sequence:

$305{,}501,\ 305{,}500, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$305{,}501,\ 305{,}500, \ \ldots$

Step-by-step solution

To solve this problem, we'll analyze the sequence pattern:

Step 1: Identify the difference between the first two numbers:
$305{,}501 - 305{,}500 = 1$ .
Step 2: Since the numbers decrease by 1 from one term to the next, apply this pattern to determine the next numbers:
Step 3: Calculate the next three numbers:

The third number: $305{,}500 - 1 = 305{,}499$
The fourth number: $305{,}499 - 1 = 305{,}498$
The fifth number: $305{,}498 - 1 = 305{,}497$

Therefore, the next three numbers in the sequence are $305{,}499, 305{,}498, 305{,}497$ .

Final Answer

$305{,}499,\ 305{,}498, \ 305{,}497$

Key Points to Remember

Essential concepts to master this topic

Pattern: Find the common difference between consecutive terms
Technique: Apply constant difference: 305,500 - 1 = 305,499
Check: Verify each term decreases by same amount: 1 ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern changes direction
Don't think the sequence will start increasing after decreasing = wrong continuation! Once you identify a decreasing pattern of -1, it continues consistently. Always maintain the same common difference throughout the sequence.

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 goes up or down?

Look at the first two terms! If the second number is smaller than the first (like 305,500 < 305,501), the sequence is decreasing. If it's larger, the sequence is increasing.

What if the difference isn't 1?

The same method works! Just find the difference between any two consecutive terms. For example, if terms decrease by 5 each time, subtract 5 from each previous term.

Do I need to show all the calculations?

Yes! Show each step: find the common difference, then apply it to get each new term. This helps you catch mistakes and shows your thinking clearly.

Can arithmetic sequences have fractions or decimals?

Absolutely! The common difference can be any number - whole numbers, fractions, or decimals. The key is that it stays constant between consecutive terms.

What if I get confused about which direction to go?

Write down what you know first: 305,501 → 305,500. The arrow shows decreasing by 1, so continue: 305,500 → 305,499 → 305,498, and so on.

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