Suppose that a function f: R → R satisfies f(x + y) = f(x)f(y) for all x, y ∈ R and f(1) = 3. If Σ???? f(i) = 363, then n is equal to
Suppose that a function f: R → R satisfies f(x + y) = f(x)f(y) for all x, y ∈ R and f(1) = 3. If Σ???? f(i) = 363, then n is equal to
Asked by Shiksha User
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1 Answer
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Given f (1) = a = 3, and assuming the function form is f (x) = a?
So f (x) = 3?
∑? f (i) = 363
⇒ 3 + 3² + . + 3? = 363
This is a geometric progression. The sum is S? = a (r? -1)/ (r-1).
3 (3? -1)/ (3-1) = 363
3 (3? -1)/2 = 363
3? - 1 = 242
3? = 243
3? = 3? ⇒ n = 5
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