Misc 7 - If f (x + y) = f(x) f(y) such that  f(1) = 3, find n - Miscellaneous

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  1. Chapter 9 Class 11 Sequences and Series
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Misc 7 If f is a function satisfying f (x + y) = f(x) f(y) for all x, y N such that f(1) = 3 and , find the value of n. Given that : f (x + y) = f(x) f(y) x, y N and f(1) = 3 f (1) = 3 f (2) = 9 = 3 2 f (3) = 27 = 3 3 f (4) = 81 = 3 4 Similarly, f (5) = 3 5 f (6) = 3 6 Thus our series is 3, 3 2 , 3 3 , 3 4 , n terms This is a GP, where a = 3 r = 3 2 3 =3 Given sum of GP = 120 = ( 1) 1 Putting a = 3, r = 3 & sum = 120 120 = 3( 3 1) 3 1 3( 3 1) 2 = 120 3 1 = 120 2 3 3 1 = 40 2 3 = 80 3 = 80 + 1 3 = 80 3 = 3 4 n = 4 n = 4

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.