Find the Next Term in Sequence: 10, 20, 25, 35, 40, ?

Q: What if none of the answer choices match my calculation?

Double-check your work! Recalculate the differences and make sure you identified the correct pattern. Also verify your arithmetic when applying the pattern.

Q: Are there other types of sequence patterns I should know?

Yes! Sequences can have constant differences (arithmetic), constant ratios (geometric), or alternating patterns like this one. Always start by finding differences between terms.

Q: Can I work backwards to check my answer?

Absolutely! If the 6th term is 50, work backwards: $ 50 - 10 = 40 $ ✓, then $ 40 - 5 = 35 $ ✓. This confirms the alternating pattern!

Arithmetic Sequences with Alternating Pattern Differences

Look at the sequence below:

$10,20,25,35,40,\text{?}$

What is the 6th element of the series?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the 6th term in the sequence

00:03 Let's observe the change between consecutive terms

00:10 We can see that the change of change is also constant, so we can calculate

00:20 We'll deduce the next terms from the pattern

00:25 Let's calculate and substitute

00:32 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the sequence below:

$10,20,25,35,40,\text{?}$

What is the 6th element of the series?

Step-by-step solution

To solve this problem, we'll determine the next term in the sequence according to a discernible pattern:

Step 1: Identify the differences between consecutive terms. The differences are $10, 5, 10, 5$ .
Step 2: Recognize the alternating pattern $+10, +5$ .
Step 3: Continue the discovered pattern after the last given term.

By examining the pattern, we see:

Starting from 40, since the last increment was $+5$ , the next increment should be $+10$ .

Therefore, the next term $40 + 10 = 50$ .

Hence, the 6th element of the series is $50$ .

The correct choice given the options is choice 4: $50$ .

Final Answer

$50$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find differences between consecutive terms to identify the pattern
Technique: Calculate differences: 10, 5, 10, 5 showing alternating +10, +5 pattern
Check: Verify pattern continues: 40 + 10 = 50, maintaining the alternating sequence ✓

Common Mistakes

Avoid these frequent errors

Adding the same difference throughout the sequence
Don't assume all differences are equal like +10 throughout = wrong pattern identification! This ignores the alternating nature and gives incorrect predictions. Always calculate each consecutive difference and look for the repeating pattern.

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 if the differences don't seem to follow a clear pattern?

Look more carefully! Sometimes patterns alternate or follow a repeating cycle. In this sequence, the differences $+10, +5, +10, +5$ repeat every two terms.

How do I know which difference to use next?

Count where you are in the pattern cycle. Since the last difference was $+5$ (from 35 to 40), and the pattern alternates $+10, +5$ , the next difference must be $+10$ .

What if none of the answer choices match my calculation?

Double-check your work! Recalculate the differences and make sure you identified the correct pattern. Also verify your arithmetic when applying the pattern.

Are there other types of sequence patterns I should know?

Yes! Sequences can have constant differences (arithmetic), constant ratios (geometric), or alternating patterns like this one. Always start by finding differences between terms.

Can I work backwards to check my answer?

Absolutely! If the 6th term is 50, work backwards: $50 - 10 = 40$ ✓, then $40 - 5 = 35$ ✓. This confirms the alternating pattern!

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