Given the series:
What is the element number 20 in the series?
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Given the series:
What is the element number 20 in the series?
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: The given series is . 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: . 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 .
5
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?
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!
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.).
Check at least 4-5 consecutive terms to confirm the pattern. Write out: and verify the alternating behavior continues.
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.
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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