In the drawing, four main structures of the series.
Choose the algebraic expression corresponding to the number of points in place of
We have hundreds of course questions with personalized recommendations + Account 100% premium
In the drawing, four main structures of the series.
Choose the algebraic expression corresponding to the number of points in place of
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Counting the points in each given structure, we observe that each subsequent structure increases the number of points in a linear fashion.
Step 2: By examining the counts, a pattern emerges where the number of points relates to the number of structures . Specifically:
- When , suppose points are 1.
- When , suppose points are 5.
- When , suppose points are 9, and so forth.
The pattern follows an arithmetic progression with a constant increment of 4 points per subsequent structure step (from to ), while starting from 1.
Step 3: Based on this pattern, the number of points can be described by the expression . This formula accounts for the consistent increase (common difference) of 4, starting from yielding the first point count.
Therefore, the solution to the problem is .
Is there a term-to-term rule for the sequence below?
18 , 22 , 26 , 30
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