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Functions question

2025 · Shift 1 · Q28

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PYQ Library
JEE Advanced
Mathematics
Functions
2025 · Shift 1 · Q28

Functions question

2025 · Shift 1 · Q28

JEE AdvancedMathematicsFunctionsNumerical+4 / −1

Let ℝ denote the set of all real numbers. Let f: ℝ → ℝ be a function such that f(x) > 0 for all x ∈ ℝ, and f(x+y) = f(x)f(y) for all x, y ∈ ℝ. Let the real numbers a₁, a₂, ..., a₅₀ be in an arithmetic progression. If f(a₃₁) = 64f(a₂₅), and

\sum\limits_{i=1}^{50} f(a_i) = 3(2^{25}+1),

then the value of

\sum\limits_{i=6}^{30} f(a_i)

is

\underline{\hspace{2cm}}

.

Numerical answer

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