Given the series:
What is the element number 20 in the series?
We have hundreds of course questions with personalized recommendations + Account 100% premium
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
Is there a term-to-term rule for the sequence below?
18 , 22 , 26 , 30
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!
Get unlimited access to all 18 Series questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime