Maths ·Class 9 Maths

Suppose P1 = 1, P2 = 2 and for n > 2, Pn = P1 + P2 + ... + Pn-1 + 1. Find the values of P1, P2, ..., P8. Class 9

RBSEGuide

· Jul 14, 2026 · Reviewed & updated Sep 17, 2026 · 1 min read

Suppose P₁ = 1, P₂ = 2 and for n > 2, P_n = P₁ + P₂ + ... + P_n-1 + 1. Find the values of P₁, P₂, ..., P₈. Class 9

Question 1.

Suppose P₁ = 1, P₂ = 2 and for n > 2, P_n = P₁ + P₂ + ... + P_n-1 + 1. Find the values of P₁, P₂, ..., P₈. Can you find a simpler recursive formula for P_n? Can you give an explicit formula? Class 9

Solution:

Given, P₁ = 1, P₂ = 2,

P_n = P₁ + P₂ + ...+ P_n-1 + 1, for n > 2

n	Pn	Recursive	Explicit
1	1	-	2⁰ = 1
2	2	-	2¹ = 2
3	1 + 2 + 1 = 4	2 × 2 = 4	2² = 4
4	1 + 2 + 4 + 1 = 8	2 × 4 = 8	2³ = 8
5	1 + 2 + 4 + 8 + 1 = 16	2 × 8 = 16	2⁴ = 16
6	1 + 2 + 4 + 8 + 16 + 1 = 32	2 × 16 = 32	2⁵ = 32
7	1 + 2 + 4 + 8 + 16 + 32 + 1 = 64	2 × 32 = 64	2⁶ = 64
8	1 + 2 + 4 + 8 + 16 + 32 + 64 + 1 = 128	2 × 64 = 128	2⁷ = 128
…	…	…	…
n	P₁ + P₂ + ….. + P_n-1 + 1	2 × P_n-1	2^n-1

Recursive Formula for P_n is

P₁ = 1, P₂ = 2

P_n = 2P_n-1, for n > 2

Explicit Formula for P_n is

P_n = 2_n-1, for n ≥ 1