If the bottom row of an n row pyramid contains the first n Virahānka-Fibonacci numbers, what can we say about the numbers in the pyramid? What can we say about the number at the top?
All numbers appearing in the pyramid will be Virahānka-Fibonacci numbers.
The number at the top will also be a Virahānka-Fibonacci number.
Reasoning: The pyramid rule (each number equals the sum of the two numbers directly below it) matches exactly with the definition of Virahānka-Fibonacci numbers, where each number is the sum of the two preceding numbers.
∴ The top number corresponds to a Virahānka-Fibonacci number further along in the sequence.
Explanation
The chapter demonstrates that the pyramid construction rule and the Virahānka-Fibonacci sequence definition are perfectly aligned. Since each VF number is the sum of the two before it, and the pyramid rule adds adjacent numbers, every number generated in the pyramid must be a VF number.
Solution Steps
The bottom row contains the first n Virahānka-Fibonacci numbers.
The pyramid rule states: each number equals the sum of the two numbers directly below it.
This rule matches the Virahānka-Fibonacci definition where each number is the sum of the two preceding numbers.
Therefore, all numbers generated in the pyramid must be Virahānka-Fibonacci numbers.
The top number is a Virahānka-Fibonacci number further along in the sequence.