First slide

Functions (XII)

Question

$Suppose that a function f : R \to R satifies f (x + y) = f (x) f (y) for all x, y \in R and f (1) = 3 . If$ $\sum_{i = 1}^{n} f (i) = 363, then n is equal to..........$

Moderate

Solution

$\begin{array}{l} f (x + y) = f (x) f (y) \\ \Rightarrow f (x) = a^{x} \\ f (x) = 3 \Rightarrow a = 3 \\ ∴ f (x) = 3^{x} \\ Now \sum_{i = 1}^{n} f (i) = 363 \\ \Rightarrow 3 + 3^{2} + 3^{3} + \dots . . nterms = 363 \\ \Rightarrow \frac{3 (3^{n} - 1)}{3 - 1} = 363 \\ \Rightarrow 3^{n} = 243 \\ \Rightarrow n = 5 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App