### Instruction: An infinite geometric series has common ratio $\frac{-1}{3}$ and sum $25.$  What is the second term of the sequence?### Response: To find the second term of the sequence, I need to know the first term.
I recall that the sum of an infinite geometric series with common ratio $r$ and first term $a$ is given by $S = \frac{a}{1-r}.$
Plugging in the given values, I get $25 = \frac{a}{1-\frac{-1}{3}}.$
Simplifying, I get $25 = \frac{3a}{4}.$
Solving for $a$, I get $a = \frac{100}{3}.$