Thus, the Virahanka-Fibonacci sequence is the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34,, where each number is the sum of the two preceding numbers.

Which of the followings isvirahanka, Fibonacci sequence

Answer: The Virahanka-Fibonacci sequence is given by the recurrence $F_n = F_{n-1} + F_{n-2}$ with $F_1 = 1, F_2 = 1$ , giving the sequence $1, 1, 2, 3, 5, 8, 13, 21, 34, 55, \dots$

Step-by-step solution

Step 1: Define the Virahanka-Fibonacci recurrence relation

The Virahanka-Fibonacci sequence is generated by adding the two preceding terms together. In ancient Indian prosody, Virahanka studied the number of poetic meters of a given duration, which leads directly to this recurrence relation.

Step 2: State the initial conditions

Starting with the initial values $F_1 = 1$ and $F_2 = 1$ (or indexed with $F_0 = 0$ and $F_1 = 1$ ), the sequence generates consecutive terms by summation: $1, 1, 2, 3, 5, 8, 13, 21, 34, \dots$

Step 3: Identify the standard sequence terms

Thus, the Virahanka-Fibonacci sequence is the sequence $1, 1, 2, 3, 5, 8, 13, 21, 34, \dots$ , where each number is the sum of the two preceding numbers.

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