80 , 60 , 40 , 20, ...
Express the term-to-term rule of this sequence in terms of n.
We have hundreds of course questions with personalized recommendations + Account 100% premium
80 , 60 , 40 , 20, ...
Express the term-to-term rule of this sequence in terms of n.
To derive the general term for the sequence 80, 60, 40, 20,..., we start by analyzing the properties of the sequence.
Step 1: Identify the first term . Here, .
Step 2: Determine the common difference . Each term decreases by 20, so .
Step 3: Use the formula for the n-th term of an arithmetic sequence: .
With these values, plug them into the formula:
Simplify the expression:
Combine like terms:
Since the expression should match one of the provided choices, adjust our perspective a bit. If matched to end at 20, reconsider from perspective of terms indicated. Ultimately correct check via choices.
Therefore, the expression of the term-to-term rule in terms of matches but reframe if choice induction error adjusted as harmonic view occuring potentially to need re-analyze structurally. Assess of sequence may differ assessment of exact query by choice.
Therefore, the solution to the problem is, per original final list analysis choice, .
Is there a term-to-term rule for the sequence below?
18 , 22 , 26 , 30
The common difference is negative (-20) because each term is smaller than the previous one. When sequences decrease, d is always negative!
The first term is simply the very first number in your sequence. Here, .
The (n-1) tells you how many times to add the common difference. For the 3rd term, you add d twice: .
Absolutely! Test several values: n=1 gives 80, n=2 gives 60, n=3 gives 40, n=4 gives 20. If they all match the original sequence, you're correct!
20n gives 20, 40, 60, 80... which is the reverse of our sequence! The correct formula gives 80, 60, 40, 20 as needed.
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