A group of students is arranging squares into layers to create a project. The first layer has 6 squares. The second layer has 12 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?
a1 = 6; an = 6 + an − 1, n > 0
a1 = 6; an = 6 ⋅ an − 1, n > 0
a1 = 6; an = 6 ⋅ an + 1, n > 0
a1 = 6; an = 6 + an + 1, n > 0
The correct formula that represents the arithmetic explicit formula to determine the number of squares in each layer is:
a1 = 6; an = 6 + an − 1, n > 0
To explain how to get this answer, let's break down the formula:
- a1 represents the first term in the sequence, which in this case is the number of squares in the first layer, given as 6.
- an represents the nth term in the sequence, which is the number of squares in the nth layer.
- n > 0 signifies that the sequence starts from the first layer and continues indefinitely.
The formula an = 6 + an − 1 indicates that to find the number of squares in each subsequent layer, you simply add 6 to the number of squares in the previous layer. This reflects the fact that each new layer in the project adds an additional 6 squares.
The correct answer is:
a1 = 6; an = 6 + an − 1, n > 0
same question here:
https://www.jiskha.com/questions/1802568/A-group-of-students-is-arranging-squares-into-layers-to-create-a-project-The-first