Find the Pattern: Analyzing the Sequence 5,10,15,20,25,30

Q: How do I know if it's addition or multiplication?

Start by checking differences between consecutive terms. If they're all the same (like +5), it's addition. If differences vary but ratios are the same, then it's multiplication.

Q: What if some differences are the same but not all?

Then there's no consistent rule for the entire sequence! A true pattern must work for every single pair of consecutive numbers in the sequence.

Q: Why isn't ×2 the answer when 5×2=10?

Because $ 10 \times 2 = 20 $, but the next term is 15, not 20! Always check if your suspected rule works for all consecutive pairs, not just the first one.

Q: How do I find the next number in this sequence?

Add 5 to the last term: $ 30 + 5 = 35 $. The rule +5 means each new term is 5 more than the previous one.

Arithmetic Sequences with Constant Differences

Look at the following set of numbers and determine if there is a rule. If there is one, what is it?

$5,10,15,20,25,30$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Do you notice any pattern here? If so, what could it be?

00:14 Let's take a closer look at how each term changes.

00:21 We see a clear pattern, adding 5 to each term.

00:34 And that's how we find the solution!

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 a rule. If there is one, what is it?

$5,10,15,20,25,30$

Step-by-step solution

To solve this problem of finding the rule for the sequence $5, 10, 15, 20, 25, 30$ , we will follow these steps:

Step 1: Analyze the difference between consecutive numbers in the sequence.
Step 2: Identify a consistent pattern or rule.
Step 3: Compare the pattern against the given multiple-choice answers.

Now, let's work through each step:

Step 1: Calculate the difference between consecutive terms:

$10 - 5 = 5$

$15 - 10 = 5$

$20 - 15 = 5$

$25 - 20 = 5$

$30 - 25 = 5$

Step 2: We observe that the difference between each pair of successive numbers is $5$ , which is consistent throughout the sequence.

Step 3: Compare this pattern with the given choices. The choice corresponding to adding 5 consistently matches our observed pattern.

Therefore, the rule for this sequence is to add 5 to each preceding number to obtain the next number in the sequence. This corresponds with choice number 2: $+5$ .

Final Answer

$+5$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find differences between consecutive terms to identify the rule
Technique: Calculate $10 - 5 = 5$ , $15 - 10 = 5$ for each pair
Verification: Check that all differences equal 5 throughout the sequence ✓

Common Mistakes

Avoid these frequent errors

Looking at multiplication patterns instead of addition
Don't assume doubling because 5×2=10 and 10×2=20 = wrong pattern! This ignores terms like 15 and 25 that don't follow doubling. Always check differences between ALL consecutive terms to find the true pattern.

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 it's addition or multiplication?

Start by checking differences between consecutive terms. If they're all the same (like +5), it's addition. If differences vary but ratios are the same, then it's multiplication.

What if some differences are the same but not all?

Then there's no consistent rule for the entire sequence! A true pattern must work for every single pair of consecutive numbers in the sequence.

Why isn't ×2 the answer when 5×2=10?

Because $10 \times 2 = 20$ , but the next term is 15, not 20! Always check if your suspected rule works for all consecutive pairs, not just the first one.

Can a sequence have more than one rule?

For simple arithmetic sequences like this one, there's typically one main rule. The pattern $+5$ consistently explains how to get from any term to the next.

How do I find the next number in this sequence?

Add 5 to the last term: $30 + 5 = 35$ . The rule +5 means each new term is 5 more than the previous one.

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