Write an explicit rule

Question

Write an explicit rule to describe the number of the shaded squares in each figure as a function of the figure number, n.

the squares go from 4 squares, to 8, to 12, to 16 as the largest square. What is the explicit rule supposed to be? Starting with a_n=

Answer 1

The number of squares is increasing by 4 each time, so this is an arithmetic sequence where the first term, a(1), is 4 and the common difference (d) is 4.

The explicit formula is a(n) = a(1) + (n-1)*d

a(n) = 4 + (n-1)*4

a(n) = 4 + 4n -4

a(n) = 4n