Let \( \mathbb{R} \) denote the set of all real numbers. Let \( f:\mathbb{R}\to\mathbb{R} \) be a function such that \( f(x)>0 \) for all \( x\in\mathbb{R} \), and \( f(x+y)=f(x)f(y) \) for all \( x,y\in\mathbb{R} \).
Let the real numbers \( a_{1},a_{2},\ldots,a_{50} \) be in an arithmetic progression. If \( f(a_{31})=64f(a_{25}) \), and then the value of \( \displaystyle \sum_{i=1}^{50} f(a_{i}) = 3\!\left(2^{25}+1\right) \), then the value of \( \displaystyle \sum_{i=6}^{30} f(a_{i}) \) is________.
