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Question Without building the entire pyramid, find the number in the topmost row given the bottom row in each of these cases.
Recall the Virahanka-Fibonacci number sequence 1, 2, 3, 5, … where each number is the sum of the two numbers before it.
(a) If a, b, c, and d are the bottom row, then the expression of the topmost row of the pyramid is a + 3b + 3c + d. Given, bottom row; Here, a = 8, b = 19, c = 21, and d = 13 ∴ The number in the topmost row = a + 3b + 3c + d = 8 + 3(19) + 3(21) + 13 = 8 + 57 + 63 + 13 = 141 Thus, the number in the topmost row is 141. (b) Given, bottom row: Here, a = 7, b = 18, c = 19 and d = 6 ∴ The number in the topmost row = a + 3b + 3c + d = 7 + 3(18) + 3(19) + 6 = 7 + 54 + 57 + 6 = 124 Thus, the number in the topmost row is 124. (c) Given, bottom row: Here, a = 9, b = 1,c = 5, and d = 11 ∴ The number in the topmost row = a + 3b + 3c + d = 9 + 3(7)+ 3(5) + 11 = 9 + 21 + 15 + 11 = 56 Thus, the number in the topmost row is 56.