jmc

The second term seems difficult to calculate directly, so we will first find the value of the first term. Let the first term be $a$. Because the sum of the series is $25,$ we have $$25=\frac{a}{1-\left(\frac{-1}{3}\right)}=\frac{a}{\frac{4}{3}}=\frac{3a}{4}.$$Thus, $a=\frac{100}{3}.$ Now, we can calculate the second term knowing the value of the first. The second term $ar$ is $$ar=\left(\frac{100}{3}\right)\left(\frac{-1}{3}\right)=\boxed{\frac{-100}{9}}.$$