jmc

First, we recognize that the number of widgets Janabel sells each day forms an arithmetic sequence. On day 1, she sells 1 widget, on day 2, she sells 3 widgets, on day 3, she sells 5 widgets, and so on. This sequence can be described by the first term $a=1$ and the common difference $d=2$. Step 1: Find the number of widgets sold on day 20 The formula for the $n$-th term of an arithmetic sequence is: $$a_n=a+(n-1)d$$ For $n=20$: $$a_{20}=1+(20-1)\cdot 2=1+38=39$$ So, Janabel sells 39 widgets on day 20. Step 2: Calculate the total number of widgets sold in 20 days} The sum $S_n$ of the first $n$ terms of an arithmetic sequence is given by: $$S_n=\frac{n}{2}\cdot (a+a_n)$$ For $n=20$: $$S_{20}=\frac{20}{2}\cdot (1+39)=10\cdot 40=400$$ Therefore, the total number of widgets sold after 20 days is: $(40\cdot 10)=\boxed{400}$