Q. 74.1( 55 Votes )

If f is a f

Answer :

Given:

f (x + y) = f (x) × f (y) for all x, y N … (1)

f (1) = 3


Taking x = y = 1 in (1), we obtain


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

Therefore, f(2) = 9

Taking x = 1 and y = 2 in (1), we obtain


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

Therefore, f(3) = 27

Similarly, Taking x = 1 and y = 3 in (1), we obtain


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

Therefore, f(4) = 81

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


We know that -


Sum of first n terms of G.P with first term 'a' and common ratio 'r' is given by -



It is known that,


This means that,
f(1) + f(2) + f(3) + .....f(n) = 120

Thus,







n = 4


Thus, the value of n is 4.

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