Find the 20th Element in the Sequence: 30,5,25,5,20...

Alternating Sequences with Pattern Recognition

Given the series:

30,5,25,5,20... 30,5,25,5,20...

What is the element number 20 in the series?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the 20th term in the sequence
00:03 We can see that the sequence of all even numbers is always equal
00:16 The 20th term is the 10th term in the second sequence
00:21 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

Given the series:

30,5,25,5,20... 30,5,25,5,20...

What is the element number 20 in the series?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the series pattern
  • Step 2: Determine where the number 5 appears in the sequence
  • Step 3: Find the 20th term in the series

Now, let's work through each step:
Step 1: The given series is 30,5,25,5,20,30, 5, 25, 5, 20, \ldots. Notice this forms a repeating pattern between decreasing numbers and the number 5.
Step 2: Observe that every odd position term (1st, 3rd, 5th, ...) is a decreasing sequence from 30 by 5: 30,25,20,30, 25, 20, \ldots. Meanwhile, every even position term in the series is 5.
Step 3: We need the 20th term. Since 20 is an even number, it corresponds to a constant "5".

Therefore, the 20th element in the series is 55.

3

Final Answer

5

Key Points to Remember

Essential concepts to master this topic
  • Pattern Rule: Odd positions decrease by 5, even positions equal 5
  • Technique: Position 20 is even, so term equals 5
  • Check: Verify pattern continues: 30,5,25,5,20,5,15,5... position 20 = 5 ✓

Common Mistakes

Avoid these frequent errors
  • Assuming the entire sequence decreases by 5
    Don't subtract 5 from every term = wrong pattern! This ignores that every even position stays at 5. Always identify which positions follow which rule in alternating sequences.

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

How do I know if a position is odd or even?

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Simply divide the position number by 2. If it divides evenly (no remainder), it's even. If there's a remainder of 1, it's odd. Position 20 ÷ 2 = 10 exactly, so it's even!

What if I need to find a term much further in the sequence?

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The same rules apply! Even positions are always 5. For odd positions, use the formula: 35 - 5n, where n is which odd position it is (1st odd, 2nd odd, etc.).

How can I be sure I identified the pattern correctly?

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Check at least 4-5 consecutive terms to confirm the pattern. Write out: 30,5,25,5,20,5,15,5... 30, 5, 25, 5, 20, 5, 15, 5... and verify the alternating behavior continues.

Why does this sequence alternate instead of just decreasing?

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This is a designed pattern where two different rules apply based on position. It's testing your ability to recognize that not all sequences follow one simple rule.

What if I miscounted the position number?

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Always double-check by listing terms with their positions: 1st=30, 2nd=5, 3rd=25, 4th=5... Count carefully to position 20. Position errors are the most common mistake!

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