If-f-x-is-a-function-satisfying-f-x-y-f-x-f-y-for-all-x-y-N-such-that-f-1-3-and-x-1-n-f-x-120-Then-the-value-of-n-is-

Question Number 26281 by kkr1729 last updated on 23/Dec/17

If f (x) is a function satisfying

f (x + y) = f (x) f (y) for all x, y \in N such

that f (1) = 3 and \underset{x = 1}{\sum^{n}} f (x) = 120 . Then

the value of n is

Answered by mrW1 last updated on 23/Dec/17

f (n + 1) = f (1) \times f (n) = 3 f (n)

\Rightarrow G . P . w i t h q = 3

3 \times \frac{3^{n} - 1}{3 - 1} = 120

3^{n} = 1 + 80 = 81 = 3^{4}

\Rightarrow n = 4

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