Number Properties: Analyzing the Sequence 1,2,3,4,5,6

Q: How do I know if a sequence has a pattern?

Start by finding the difference between consecutive terms. If all differences are the same, you have an arithmetic sequence! Even simple patterns like +1 or +2 count as valid properties.

Q: Is +1 really a significant pattern?

Absolutely! The sequence $ 1,2,3,4,5,6 $ represents consecutive integers, which is a fundamental arithmetic sequence. Don't dismiss simple patterns!

Q: How do I calculate the common difference correctly?

Always subtract in order: next term minus current term. So for 1,2,3: calculate $ 2-1=1 $, then $ 3-2=1 $. Keep the same order throughout!

Q: What if I get negative differences?

That's fine! A common difference of $ -2 $ means the sequence decreases by 2 each time. Negative differences are just as valid as positive ones.

Arithmetic Sequences with Consecutive Integers

Look at the following set of numbers and determine if there is any property, if so, what is it?

$1,2,3,4,5,6$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is there any pattern? And if so, what is it?

00:03 Let's observe the change between terms

00:11 We can see that the pattern is constant and it's adding 1

00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following set of numbers and determine if there is any property, if so, what is it?

$1,2,3,4,5,6$

Step-by-step solution

To solve this problem, we need to determine if there's a consistent pattern or rule in the sequence $1, 2, 3, 4, 5, 6$ .

Let's proceed step by step:

Step 1: Analyze the given sequence
The sequence is $1, 2, 3, 4, 5, 6$ .
Step 2: Check for a common difference
Calculate the difference between each consecutive pair of numbers:

$2 - 1 = 1$
$3 - 2 = 1$
$4 - 3 = 1$
$5 - 4 = 1$
$6 - 5 = 1$

From the calculations above, we observe that the difference between each consecutive term is $+1$ .

Conclusion: The sequence is an arithmetic sequence with a common difference of $+1$ .

Therefore, the correct choice is $+1$ .

Final Answer

$+1$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Calculate differences between consecutive terms to identify sequence type
Technique: Find common difference: $2-1=1, 3-2=1, 4-3=1$
Check: Verify all consecutive differences equal +1 throughout the sequence ✓

Common Mistakes

Avoid these frequent errors

Assuming no pattern exists without checking differences
Don't conclude 'no pattern exists' without calculating consecutive differences = missing obvious arithmetic sequences! Students often overlook simple patterns like +1. Always subtract each term from the next term to find the common difference.

Practice Quiz

Test your knowledge with interactive questions

Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

FAQ

Everything you need to know about this question

How do I know if a sequence has a pattern?

Start by finding the difference between consecutive terms. If all differences are the same, you have an arithmetic sequence! Even simple patterns like +1 or +2 count as valid properties.

What if the differences aren't all the same?

Then it's not an arithmetic sequence, but there might be other patterns! Try looking at ratios between terms, or check if differences form their own pattern.

Is +1 really a significant pattern?

Absolutely! The sequence $1,2,3,4,5,6$ represents consecutive integers, which is a fundamental arithmetic sequence. Don't dismiss simple patterns!

How do I calculate the common difference correctly?

Always subtract in order: next term minus current term. So for 1,2,3: calculate $2-1=1$ , then $3-2=1$ . Keep the same order throughout!

What if I get negative differences?

That's fine! A common difference of $-2$ means the sequence decreases by 2 each time. Negative differences are just as valid as positive ones.

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