Analyze the Sequence 13, 10, 7, 4, 1: Identifying Number Patterns

Q: What does a negative common difference mean?

A negative common difference means the sequence is decreasing! Each term gets smaller by the same amount. In our sequence, each number is 3 less than the previous one.

Q: How do I know which number to subtract from which?

Always use the formula: next term - current term. So for 13, 10: calculate 10 - 13 = -3. This keeps the order consistent and gives the correct sign.

Q: What if I get different differences between terms?

If the differences aren't all the same, then it's not an arithmetic sequence! The sequence might follow a different pattern, or have no pattern at all.

Q: Can arithmetic sequences have positive and negative numbers?

Absolutely! Arithmetic sequences can include any real numbers - positive, negative, fractions, or decimals. What matters is that the common difference stays the same.

Q: How do I continue this sequence?

Keep subtracting 3! After 1 comes: $ 1 - 3 = -2 $, then $ -2 - 3 = -5 $, and so on. The pattern continues forever.

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

00:08 We can see that the pattern is constant and it's adding 3

00:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

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

$13,10,7,4,1$

2

Step-by-step solution

To solve this problem, we will determine if the given sequence of numbers follows a particular pattern or property:

First, we list the sequence provided: $13, 10, 7, 4, 1$ .

Since an arithmetic sequence is one of the simplest patterns, we will check for a common difference, which involves subtracting each term from the next:

Calculate the difference between the first and second terms: $10 - 13 = -3$ .
Calculate the difference between the second and third terms: $7 - 10 = -3$ .
Calculate the difference between the third and fourth terms: $4 - 7 = -3$ .
Calculate the difference between the fourth and fifth terms: $1 - 4 = -3$ .

We observe that the difference between each consecutive pair of numbers is consistently $-3$ . This implies that the sequence has a common difference of $-3$ , and therefore, it is an arithmetic sequence.

In conclusion, the identified property for the sequence is that it is an arithmetic sequence with a common difference of $-3$ .

Therefore, the solution to the problem is $-3$ .

3

Final Answer

$-3$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the difference between consecutive terms consistently
Technique: Calculate $10 - 13 = -3$ , then verify with other pairs
Check: All differences equal $-3$ : decreasing by 3 each time ✓

Common Mistakes

Avoid these frequent errors

Calculating differences in wrong order
Don't subtract the first term from the second (13 - 10 = +3) = wrong sign! This gives a positive difference when the sequence is actually decreasing. Always calculate second term minus first term (10 - 13 = -3).

Practice Quiz

Test your knowledge with interactive questions

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

FAQ

Everything you need to know about this question

What does a negative common difference mean?

+

A negative common difference means the sequence is decreasing! Each term gets smaller by the same amount. In our sequence, each number is 3 less than the previous one.

How do I know which number to subtract from which?

+

Always use the formula: next term - current term. So for 13, 10: calculate 10 - 13 = -3. This keeps the order consistent and gives the correct sign.

What if I get different differences between terms?

+

If the differences aren't all the same, then it's not an arithmetic sequence! The sequence might follow a different pattern, or have no pattern at all.

Can arithmetic sequences have positive and negative numbers?

+

Absolutely! Arithmetic sequences can include any real numbers - positive, negative, fractions, or decimals. What matters is that the common difference stays the same.

How do I continue this sequence?

+

Keep subtracting 3! After 1 comes: $1 - 3 = -2$ , then $-2 - 3 = -5$ , and so on. The pattern continues forever.

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Analyze the Sequence 13, 10, 7, 4, 1: Identifying Number Patterns

Arithmetic Sequences with Negative Common Differences

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