JEE Advance 2025 Paper 1

Let $f(x) > 0$   and $f(x+y) = f(x)f(y)$  . Let $a_{1}, ..., a_{50}$   be in AP. If $f(a_{31}) = 64f(a_{25})$   and $\sum_{i=1}^{50} f(a_{i}) = 3(2^{25} + 1)$  , find $\sum_{i=6}^{30} f(a_{i})$  .