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Solution for If F is a Function Satisfying F (X +Y) = F(X) F(Y) for All X, Y ∈ N Such That F(1) = 3 and `Sum_(X = 1)^N` F(X) = 120, Find the Value of N. - CBSE (Arts) Class 11 - Mathematics

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Question

If f is a function satisfying f (x +y) = f(x) f(y) for all x, y ∈ N such that f(1) = 3 and `sum_(x = 1)^n` f(x) = 120, find the value of n.

Solution

It is given that,

(x + y) = (x) × (y) for all xy ∈ N … (1)

(1) = 3

Taking x = y = 1 in (1), we obtain

f (1 + 1) = (2) = (1) (1) = 3 × 3 = 9

Similarly,

(1 + 1 + 1) = (3) = (1 + 2) = (1) (2) = 3 × 9 = 27

(4) = (1 + 3) = f (1) (3) = 3 × 27 = 81

∴ (1), (2), (3), …, that is 3, 9, 27, …, forms a G.P. with both the first term and common ratio equal to 3.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Mathematics Textbook for Class 11 (with solutions)
Chapter 9: Sequences and Series
Q: 7 | Page no. 199
Solution for question: If F is a Function Satisfying F (X +Y) = F(X) F(Y) for All X, Y ∈ N Such That F(1) = 3 and `Sum_(X = 1)^N` F(X) = 120, Find the Value of N. concept: Geometric Progression (G. P.). For the courses CBSE (Arts), CBSE (Science), CBSE (Commerce)
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