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f(x+y)=f(x)+f(y)...............∑ f(x)=84 (upto n terms......starting from x=1)...........f(1)=3.............then find n....PLS EXPLAIN THIS QUESTION >>>>.........

f(x+y)=f(x)+f(y)...............∑ f(x)=84 (upto n terms......starting from x=1)...........f(1)=3.............then find n....PLS EXPLAIN THIS QUESTION >>>>.........

Grade:9

1 Answers

jitender lakhanpal
62 Points
10 years ago

Dear Shivam,

 

f(x+y)=f(x)+f(y)  put x = y = 1      f(1) = 3

f(2) = 6

 put   x= 1, y = 2

f(3) = 9

similarly f(4) = 12

so this is an A.P starting from 3  and the common difference is also 3 

the 

∑ f(x)=84   starting from 1 is the sum of first n terms 

so by the formula 

84 = n/2[2a + (n-1)d]

so putting the values we get the quadratic in n

n2 + n - 56 = 0

so solving we get the value of n = 7

 

 

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