Calculating values gives 1, 2, 3, 5, 8, 13, 21, 34. Subtracting consecutive terms reveals Wn – Wn-1 = Wn-2, which means Wn = Wn-1 + Wn-2. This is the Virahanka-Fibonacci sequence.
Suppose W1 = 1, W2 = 2 and for n > 2, Wn = W1 + W2 + ··· + Wn-2 + 2. Find the values of W1, W2, …, W8. Do you recognise this sequence?
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Given W1 = 1, W2 = 2 and Wn = W1 + … + Wn-2 + 2:
W3 = W1 + 2 = 1 + 2 = 3
W4 = (1 + 2) + 2 = 5
W5 = (1 + 2 + 3) + 2 = 8
W6 = 8 + 5 = 13
W7 = 13 + 8 = 21
W8 = 21 + 13 = 34.
The first eight values are: 1, 2, 3, 5, 8, 13, 21, 34.
Notice that Wn – Wn-1 = Wn-2, which gives Wn = Wn-1 + Wn-2.
This is the Virahanka-Fibonacci sequence.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 8 Predicting What Comes Next: Exploring Sequences and Progressions Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-8/