Complete the Sequence: Finding the Pattern in 4,580, 4,570, 4,560,...

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

Look at the first few terms! If each number is smaller than the previous one (like 4,580 → 4,570), the sequence is decreasing. If each number gets larger, it's increasing.

Q: What if the difference isn't the same between all terms?

Then it's not an arithmetic sequence! Always check that the difference is constant between consecutive terms before continuing the pattern.

Q: Do I subtract 10 or subtract from 10?

You subtract 10 from each term! So 4,560 - 10 = 4,550, then 4,550 - 10 = 4,540, and so on. Don't subtract the term from 10.

Q: Why is the answer 4,550, 4,540, 4,530 and not something else?

Because the pattern shows a constant decrease of 10. Starting from 4,560, we subtract 10 three times: $ 4,560 - 10 = 4,550 $, $ 4,550 - 10 = 4,540 $, $ 4,540 - 10 = 4,530 $.

Q: Can arithmetic sequences have negative differences?

Absolutely! When the common difference is negative (like -10 in this problem), the sequence decreases. Positive differences make sequences increase.

Arithmetic Sequences with Constant Differences

Complete the sequence:

$4{,}580,\ 4{,}570,\ 4{,}560, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$4{,}580,\ 4{,}570,\ 4{,}560, \ \ldots$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the difference between each given term in the sequence.
Step 2: Confirm this difference is consistent across the initial sequence.
Step 3: Use this pattern to determine the next terms.

Now, let's work through each step:

Step 1: Calculate the difference between the first two terms: $4580 - 4570 = 10$ .

Step 2: Confirm the difference between the next terms is the same: $4570 - 4560 = 10$ . This confirms a constant decrement of 10.

Step 3: Continue the sequence using this pattern:

The next term is $4560 - 10 = 4550$ .
The following term is $4550 - 10 = 4540$ .
The final term in this sequence is $4540 - 10 = 4530$ .

The next three terms in the sequence are $4550, 4540, 4530$ .

Therefore, the correct answer according to the provided choices is: $4550, 4540, 4530$ , which corresponds to choice 4.

Final Answer

$4{,}550,\ 4{,}540,\ 4{,}530$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference between consecutive terms
Technique: Calculate 4,580 - 4,570 = -10 for each step
Check: Verify pattern holds: 4,570 - 4,560 = -10 consistently ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting the common difference
Don't add 10 to continue the sequence when numbers are decreasing = wrong direction! This happens when you ignore the negative sign in the difference. Always subtract 10 from each term when the sequence is decreasing.

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 if the sequence is increasing or decreasing?

Look at the first few terms! If each number is smaller than the previous one (like 4,580 → 4,570), the sequence is decreasing. If each number gets larger, it's increasing.

What if the difference isn't the same between all terms?

Then it's not an arithmetic sequence! Always check that the difference is constant between consecutive terms before continuing the pattern.

Do I subtract 10 or subtract from 10?

You subtract 10 from each term! So 4,560 - 10 = 4,550, then 4,550 - 10 = 4,540, and so on. Don't subtract the term from 10.

Why is the answer 4,550, 4,540, 4,530 and not something else?

Because the pattern shows a constant decrease of 10. Starting from 4,560, we subtract 10 three times: $4,560 - 10 = 4,550$ , $4,550 - 10 = 4,540$ , $4,540 - 10 = 4,530$ .

Can arithmetic sequences have negative differences?

Absolutely! When the common difference is negative (like -10 in this problem), the sequence decreases. Positive differences make sequences increase.

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