Agroup 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

Step-by-step 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

(Answer)

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.