
Call Us
+91 8076753736 
Send us an Email
[email protected]
Permutations And Combinations
If f is a function f(x + y) = f(x) f(y) for all x, y N such that f(1) = 3 and , find the value of n.
Given f(1) = 3
and f(x + y) = f(x). f(y) ...(ii) x, ...(i)
Putting x = 1, y = 1 in (ii), we get
f(1 + 1) = f(1). f(1) f(2) = 3. 3 = 9.
Putting x = 1, y = 2 in (ii), we get
f(1 + 2) = f(1). f(2) = 3 . 9 = 27 or f(3) = 27
Putting x = 1, y = 3 in (ii), we get
f(1 + 3) = f(1). f(3) = 3. 27 = 81 or f(4) = 81
∴ f(1) = 3, f(2) = 9, f(3) = 27, f(4) = 81, ...............
Here, the sequence 3, 9, 27, 81, .................. is a G.P. with a = 3, r = 3.
Now,
or 3 + 9 + 27 +............ to n terms = 120
∴ n = 4
Sponsor Area
Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.
Sponsor Area