JEE Advance 2025 Paper 1

Let $f(x+y)=f(x)f(y)$   with $f(x)>0$  . Let $a_1, \dots, a_{50}$   be in AP. If $f(a_{31}) = 64f(a_{25})$   and $\sum_{i=1}^{50} f(a_i) = 3(2^{25} + 1)$  , find $\sum_{i=6}^{30} f(a_i)$  .