Complete the Sequence: Finding the Pattern in 176, 175, 174

Q: How do I know if a sequence is arithmetic?

Check if the difference between consecutive terms is the same! In $ 176, 175, 174 $, each term decreases by exactly 1, so it's arithmetic with common difference -1.

Q: What if the numbers were going up instead of down?

The same principle applies! If you had $ 174, 175, 176 $, you'd be adding 1 to each term. The pattern is still arithmetic, just with a positive common difference.

Q: Do I always subtract 1 in these problems?

No! The common difference depends on the given sequence. You could subtract 2, add 3, or have any constant difference. Always calculate the difference first.

Q: How many terms should I find?

Look at the answer choices! In this problem, you need 4 more terms after 174 to match the options: 173, 172, 171, 170.

Q: What if I can't see a pattern right away?

Start by finding differences: $ 175 - 176 = -1 $ and $ 174 - 175 = -1 $. When differences are equal, you have an arithmetic sequence!

Arithmetic Sequences with Decreasing Integers

Complete the sequence:

$176,175,174,\ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$176,175,174,\ldots$

Step-by-step solution

To solve this problem, let's follow these steps:

Step 1: Identify the pattern in the given sequence.
Step 2: Recognize that the sequence decreases each term by 1.
Step 3: Continue subtracting 1 from each term to extend the sequence.

Now, let's perform each step:

Step 1: The given sequence is $176, 175, 174$ . Observing these numbers, each term is exactly 1 less than the previous term.

Step 2: We can confirm the pattern is subtracting 1 from the preceding term.

Step 3: Continue this pattern with subsequent terms:

After 174, the next term is $174 - 1 = 173$ .
After 173, the next term is $173 - 1 = 172$ .
After 172, the next term is $172 - 1 = 171$ .
After 171, the next term is $171 - 1 = 170$ .

Therefore, by following the identified pattern, we extend the sequence as $173, 172, 171, 170$ .

The correct answer is $\mathbf{173, 172, 171, 170}$ .

Final Answer

$173,172,171,170$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Identify the common difference between consecutive terms
Technique: Subtract 1 from each term: 174 - 1 = 173
Check: Verify pattern holds: 176 → 175 → 174 → 173 ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern changes or gets more complex
Don't look for complicated patterns when a simple one exists = wrong sequence! Students often overthink and miss that 176, 175, 174 simply decreases by 1 each time. Always check if the difference between consecutive terms is constant first.

Practice Quiz

Test your knowledge with interactive questions

Complete the following sequence:

$1,3.\ldots$

FAQ

Everything you need to know about this question

How do I know if a sequence is arithmetic?

Check if the difference between consecutive terms is the same! In $176, 175, 174$ , each term decreases by exactly 1, so it's arithmetic with common difference -1.

What if the numbers were going up instead of down?

The same principle applies! If you had $174, 175, 176$ , you'd be adding 1 to each term. The pattern is still arithmetic, just with a positive common difference.

Do I always subtract 1 in these problems?

No! The common difference depends on the given sequence. You could subtract 2, add 3, or have any constant difference. Always calculate the difference first.

How many terms should I find?

Look at the answer choices! In this problem, you need 4 more terms after 174 to match the options: 173, 172, 171, 170.

What if I can't see a pattern right away?

Start by finding differences: $175 - 176 = -1$ and $174 - 175 = -1$ . When differences are equal, you have an arithmetic sequence!

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