Question

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

Answer 1

`a_(1) = 6, a_(n) = 6 + a_(n - 1), n > 0`

Explanation:

In the first layer, there are 6 squares. The second layer has 12 squares.

So, the second term is 6 more than the first term i.e., in general, the number of squares in a layer is 6 greater than the number of squares in its previous layer,

If we generalize this A.P. as arithmetic explicit formula then it becomes

`a_(1) = 6, a_(n) = 6 + a_(n - 1), n > 0` (Answer)