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Question What can you say about the numbers in the pyramid and the number at the top in the following cases?
(i) The first four Virahanka-Fibonacci numbers are written in the bottom row of a four-row pyramid.
(ii) The first 29 Virahanka-Fibonacci numbers are written in the bottom row of a 29-row pyramid.
(i) We know that, The first four Virahanka-Fibonacci numbers = 1, 2, 3, 5 Here, the bottom row Let a, b, c, d, e, and f be the missing numbers. d = 1 + 2 = 3 e = 2 + 3 = 5 f = 3 + 5 = 8 b = d + e = 3 + 5 = 8 c = e + f = 5 + 8 = 13 and a = b + c = 8 + 13 = 21 The numbers in the pyramid are 1, 2, 3, 5, 8, 8, 13, 21,…. We can say that the numbers are a Virahanka-Fibonacci sequence. ∴ The number at the top = 21 (ii) From the above solution, we get The number at the top = 2 × (Total number of digits present at the bottom) – 1 = 2x – 1 = 2 × 29 – 1 = 58 – 1 = 57th Fibonacci numbers.