Computing terms yields 1, 2, 4, 8, 16, 32, 64, 128. Since Pn – Pn-1 = Pn-1, the simpler recursive rule is Pn = 2Pn-1 for n >= 3. The explicit formula is Pn = 2ⁿ⁻¹ for n >= 2 with P1 = 1.
Suppose P1 = 1, P2 = 2 and for n > 2, Pn = P1 + P2 + ··· + Pn-1 + 1. Find the values of P1, P2, …, P8. Can you find a simpler recursive formula for Pn? Can you give an explicit formula?
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Given P1 = 1, P2 = 2 and Pn = P1 + P2 + … + Pn-1 + 1:
P3 = 1 + 2 + 1 = 4
P4 = 4 + 4 = 8
P5 = 8 + 8 = 16
P6 = 32, P7 = 64, P8 = 128.
Values are: 1, 2, 4, 8, 16, 32, 64, 128.
Simpler recursive rule:
Pn = (P1 + … + Pn-2 + 1) + Pn-1 = Pn-1 + Pn-1 = 2Pn-1 for n >= 3 (with P1 = 1, P2 = 2).
Explicit formula:
P1 = 1 and Pn = 2ⁿ⁻¹ for all n >= 2.
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/