Q. 74.1( 55 Votes )

# If f is a f

Answer :

Given:

f (x + y) = f (x) × f (y) for all x, y N … (1)

f (1) = 3

Taking x = y = 1 in (1), we obtain

f (1 + 1) = f (2) = f (1) f (1) = 3 × 3 = 9

Therefore, f(2) = 9

Taking x = 1 and y = 2 in (1), we obtain

f (1 + 2) = f (3) = f (1) f (2) = 3 × 9 = 27

Therefore, f(3) = 27

Similarly, Taking x = 1 and y = 3 in (1), we obtain

f (1 + 3) = f (4) = f (1) f (3) = 3 × 27 = 81

Therefore, f(4) = 81

f (1), f (2), f (3), …, that is 3, 9, 27, …, forms a G.P. with both the first term and common ratio equal to 3.

We know that -

Sum of first n terms of G.P with first term 'a' and common ratio 'r' is given by - It is known that, This means that,
f(1) + f(2) + f(3) + .....f(n) = 120

Thus,      n = 4

Thus, the value of n is 4.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

The product of thRD Sharma - Mathematics

Express <imRS Aggarwal - Mathematics

If a, b, c are inRS Aggarwal - Mathematics

Express <imRS Aggarwal - Mathematics

Prove that RS Aggarwal - Mathematics

If a, b, c are inRS Aggarwal - Mathematics

The sum of n termRS Aggarwal - Mathematics

If a, b, c, d areRS Aggarwal - Mathematics

Evaluate :
</p
RS Aggarwal - Mathematics

The first term ofRS Aggarwal - Mathematics