### Instruction: An infinite geometric series has common ratio $-1/5$ and sum $16.$  What is the first term of the series?### Response: I know that the formula for the sum of an infinite geometric series is $S = \frac{a}{1-r},$ where $a$ is the first term and $r$ is the common ratio.
In this problem, I am given that $S = 16$ and $r = -1/5,$ so I can plug those values into the formula and solve for $a.$
I get $16 = \frac{a}{1-(-1/5)} = \frac{a}{6/5} = \frac{5a}{6}.$
Multiplying both sides by $6,$ I get $96 = 5a.$
Dividing both sides by $5,$ I get $a = 96/5 = 19.2.$