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

Explanation

Given,`f(x+y)=f(x)f(y)`


Substituting y=1:


`f(x+1)=3f(x)`
`(∵f(1)=3)`
`⟹f(x)f(x+1)​=3`


The above shows that the ratio of two consecutive terms of f(x) when x∈N is constant.

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