Question 5 - Figure it out - Page 140 - Chapter 6 Class 8 - Algebra Play (Ganita Prakash II)

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Question 5 What can you say about the numbers in the pyramid and the number at the top in the following cases? (i) The first four Virahāṅka-Fibonacci numbers are written in the bottom row of a four row pyramid.The Virahānka-Fibonacci Numbers sequence is: 1, 2, 3, 5, 8, 13, 21, 34 … Writing first four numbers : 1, 2, 3, 5 in the bottom row of our Pyramid We get the Pyramid like So, Filled pyramid looks like We notice that every single number inside the pyramid belongs to the Virahānka-Fibonacci sequence. And, The top number is 21 Which is the 7th number in the sequence Question 5 What can you say about the numbers in the pyramid and the number at the top in the following cases? (ii) The first 29 Virahāṅka-Fibonacci numbers are written in the bottom row of a 29 row pyramid.We can't easily draw 29 rows, but we can use the position pattern we discovered: 2 rows → Top is the 3rd number (3) 3 rows → Top is the 5th number (8) 4 rows → Top is the 7th number (21) Thus, we can see a rule emerging Position of top number = 2 × Number of bottom rows – 1 For 29 bottom rows Position of top number = 2 × Number of bottom rows – 1 = 2 × 29 – 1 = 58 – 1 = 57 Thus, the top number is the 57th Virahānka-Fibonacci number