NCERT Class XI Mathematics - Sequences and Series - Solutions
© examsnet.com
Question : 85
Total: 106
If f is a function satisfying f (x + y) = f (x) f (y) for all x, y ∈ N such that f (1) = 3 and
f ( x )
Solution:
We are given
f (x + y) = f (x) f (y) ∀ x, y ∈ N ....(i)
f (1) = 3 ,
∴ f (2) = f (1 + 1) = f (1) f (1) = 3·3 =3 2
f (3) = f (2 + 1) = f (2)· f (1) =3 2 3 3
Proceeding like above, we get f (n) =3 n
We have
⇒ f (1) + f (2) + ...... + f (n) = 120 ⇒ 3 +3 2 3 n
⇒
3 ( 3 n − 1 )
⇒3 n − 1 3 n 3 n ( 3 ) 4
∴ n = 4
f (x + y) = f (x) f (y) ∀ x, y ∈ N ....(i)
f (1) = 3 ,
∴ f (2) = f (1 + 1) = f (1) f (1) = 3·3 =
f (3) = f (2 + 1) = f (2)· f (1) =
Proceeding like above, we get f (n) =
We have
⇒ f (1) + f (2) + ...... + f (n) = 120 ⇒ 3 +
⇒
⇒
∴ n = 4
© examsnet.com
Go to Question: