Question 3 - Figure it out - Page 140 - Chapter 6 Class 8 - Algebra Play (Ganita Prakash II)

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Question 3 Without building the entire pyramid, find the number in the topmost row given the bottom row in each of these cases. Recall the Virahāṅka-Fibonacci number sequence 1, 2, 3, 5, … where each number is the sum of the two numbers before it.We know that for a general pyramid with 4 rows at the bottom Pyramid 1 Top most value = 8 + 3 × 19 + 3 × 21 + 13 = 8 + 57 + 63 + 13 = 141 Pyramid 2 Top most value = 7 + 3 × 18 + 3 × 19 + 6 = 7 + 54 + 57 + 6 = 124 Pyramid 3 Top most value = 9 + 3 × 7 + 3 × 5 + 11 = 9 + 21 + 15 + 11 = 56 Virahānka-Fibonacci Numbers Section In Virahānka-Fibonacci Numbers, each number is sum of the previous two numbers The sequence is: 1, 2, 3, 5, 8, 13, 21, 34 … In a way, Number Pyramid is also the same thing