### Instruction: An infinite geometric series has common ratio $\frac{-1}{3}$ and sum $25.$  What is the second term of the sequence?### Response: Let's call the first term of the sequence x.
And since the common ratio is $\frac{-1}{3}$, the second term will be $\frac{-1}{3}x$.
Right. Now we use the formula for the sum of an infinite geometric series, which is $\frac{a}{1-r}$.
This gives us $\frac{x}{1+\frac{1}{3}}=25$.
Simplifying the left side gives us $\frac{3x}{4}=25$.
So $3x=100$ and $x=\frac{100}{3}$.
Therefore, $\frac{-1}{3}x=\frac{-100}{9}$.