Final answer:
The arithmetic explicit formula to determine the number of squares in each layer, with the first layer having 5 squares and the subsequent layers adding 5 more squares each, is an = 5n.
Step-by-step explanation:
The student is asking for an arithmetic explicit formula to determine the number of squares in each layer of a project, given that the first layer has 5 squares and the second layer has 10 squares. This problem involves understanding arithmetic sequences, which is a sequence of numbers with a common difference between consecutive terms.
To find the explicit formula for an arithmetic sequence, we can use the formula:
an = a1 + (n - 1)d,
where an is the nth term, a1 is the first term, n is the term number, and d is the common difference between the terms.
In this case, since the first term a1 (the number of squares in the first layer) is 5 and the second term is 10, we can find the common difference by subtracting the first term from the second term:
d = 10 - 5 = 5.
Therefore, the explicit formula for the number of squares in the nth layer is:
an = 5 + (n - 1) * 5 or an = 5n.