Given a series whose first element is 15, each element of the series is less by 2 of its predecessor.
Is the number 1 an element of the series?
We have hundreds of course questions with personalized recommendations + Account 100% premium
Given a series whose first element is 15, each element of the series is less by 2 of its predecessor.
Is the number 1 an element of the series?
We know that the first term of the series is 15.
From here we can easily write the entire series, until we see if we reach 1.
15, 13, 11, 9, 7, 5, 3, 1
The number 1 is indeed an element of the series!
Yes
Is there a term-to-term rule for the sequence below?
18 , 22 , 26 , 30
If n is negative or a fraction, then the number is not in the sequence! Only positive integers for n mean the number exists as a term in the sequence.
The common difference is how much you add or subtract to get the next term. In this problem, each term is 2 less than the previous, so d = -2.
While listing works for short sequences, it's inefficient and error-prone. Using the formula is faster and works for any sequence length!
This means: Does 1 appear as one of the terms? We need to determine if there's some position n where the nth term equals exactly 1.
Solving algebraically is more reliable and works even when the sequence has hundreds of terms. It also proves definitively whether the number exists or not.
That means 1 is the 8th term in the sequence! You can verify: ✓
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