Final answer:
Sherry will have sold a total of 400 fidget spinners by the 20th day, as her daily sales follow an arithmetic sequence starting at 1 and increasing by 2 each day.
Step-by-step explanation:
To determine how many fidget spinners Sherry will have sold by the 20th day, we notice that the number of spinners sold each day follows an arithmetic sequence, where each day she sells 2 more than the previous day. The first term a1 of this sequence is 1 (the number of spinners sold on day one), and the common difference d is 2 (the amount by which the sales increase each day).
The nth term an of an arithmetic sequence can be found using the formula:
an = a1 + (n - 1) * d
Using this formula, the number of fidget spinners sold on the 20th day would be:
a20 = 1 + (20 - 1) * 2 = 1 + 38 = 39
To find the total number of fidget spinners sold by the 20th day, we need to calculate the sum of the first 20 terms of the arithmetic sequence, which can be done using the following formula:
Sum = n/2 * (2a1 + (n - 1) * d)
For Sherry's sales, this gives us:
Sum = 20/2 * (2*1 + (20 - 1) * 2) = 10 * (2 + 38) = 10 * 40 = 400
Therefore, Sherry will have sold 400 fidget spinners by the 20th day.