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Question

If f(x+y)=f(x)f(y) for all x,y ϵ R,f(1)=2 and nk=1f(4+k)=480, then n=

A
2
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B
4
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C
6
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D
8
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Solution

The correct option is C 4
On observation, we can say that
f(x)=abx
f(1)=2=ab
Now, nk=1f(4+k)=f(5)+f(6)+f(7+).....+f(4+n)=480
so, a5b+a6b+a7b+....+a(4+n)b=480
25+26+27+.....+2(4+n)=480
Using GP we get
25(2m+45+11)21=4802n=16
So, n=4

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