Find the Pattern in the Sequence: 715,347, 714,347, ...

Q: How do I know if I found the right pattern?

Check if the same difference works between all given terms. In this case, $ 715,347 - 714,347 = 1,000 $, so each term should be 1,000 less than the previous one.

Q: What if the numbers are decreasing? Is that still a pattern?

Absolutely! Decreasing sequences are just as valid. The common difference is simply negative. Here, we subtract 1,000 each time, which means the common difference is -1,000.

Q: What if I made an arithmetic error in subtraction?

Always double-check your subtraction! With large numbers like 715,347, it's easy to make mistakes. Try the calculation twice or use the pattern to verify: does $ 714,347 - 1,000 = 713,347 $?

Q: How many terms should I find to complete the sequence?

Look at what the question asks for! Usually it's the next few terms. In multiple choice questions like this, find enough terms to match one of the given options.

Arithmetic Sequences with Decreasing Terms

Complete the sequence:

$715{,}347,\ 714{,}347, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$715{,}347,\ 714{,}347, \ \ldots$

Step-by-step solution

To solve the sequence problem, we follow these steps:

Step 1: Determine the pattern of the sequence by finding the common difference.
Step 2: Use the common difference to find the next terms.

Step 1: The first number in the sequence is 715,347, and the second is 714,347. Subtract the second from the first:
$715,347 - 714,347 = 1,000$ .
This indicates that each term is 1,000 less than the previous term.

Step 2: To find the next numbers in the sequence, continue subtracting 1,000 from the last known term:
- Third term: $714,347 - 1,000 = 713,347$ .
- Fourth term: $713,347 - 1,000 = 712,347$ .
- Fifth term: $712,347 - 1,000 = 711,347$ .

Thus, the next three terms in the sequence are $713,347$ , $712,347$ , and $711,347$ .

Therefore, the correct completion of the sequence is: $713,347, 712,347, 711,347$ .

Final Answer

$713{,}347,\ 712{,}347, \ 711{,}347$

Key Points to Remember

Essential concepts to master this topic

Pattern Rule: Find the common difference between consecutive terms
Technique: Subtract next from previous: $715,347 - 714,347 = 1,000$
Check: Verify pattern continues: $714,347 - 713,347 = 1,000$ ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern changes direction or involves multiple operations
Don't think the sequence switches to adding or involves complex calculations = wrong continuation! Once you find the common difference, it stays constant throughout the sequence. Always apply the same difference to find each next term.

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 I found the right pattern?

Check if the same difference works between all given terms. In this case, $715,347 - 714,347 = 1,000$ , so each term should be 1,000 less than the previous one.

What if the numbers are decreasing? Is that still a pattern?

Absolutely! Decreasing sequences are just as valid. The common difference is simply negative. Here, we subtract 1,000 each time, which means the common difference is -1,000.

Do I need to find a formula for the sequence?

Not necessarily! For this type of question, you just need to continue the pattern. However, knowing the formula $a_n = 715,347 - 1,000(n-1)$ can help verify your work.

What if I made an arithmetic error in subtraction?

Always double-check your subtraction! With large numbers like 715,347, it's easy to make mistakes. Try the calculation twice or use the pattern to verify: does $714,347 - 1,000 = 713,347$ ?

Can sequences have patterns other than adding or subtracting?

Yes! Some sequences multiply, divide, or follow more complex patterns. But this question shows arithmetic sequences where we add or subtract the same amount each time.

How many terms should I find to complete the sequence?

Look at what the question asks for! Usually it's the next few terms. In multiple choice questions like this, find enough terms to match one of the given options.

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