Question

What is the recursive formula for the amount of boxes?

Answer 1

Explanation:

Let the box be x

x¹ = 1

x ² = 4

x³ = 9

Here, we can notice that the no. of boxes are in the term of square .

x n = (2n-1 ) + an - 1 is the formula

x ¹ = 1

x ² = (2 × 2 - 1) + 1 = 4

x ³ = ( 2 ×3 -1 ) + 4 = 9

x ⁴ = ( 2 × 4 - 1 ) + 9 = 16

Answer 2

an = (2n-1) + a(n-1)

a1 =1

Explanation:

a1 =1

a2 = 4

a3 = 9

We can see that the number of boxes is the term number squared

an = n^2 is the explicit formula

an = (2n-1) + an-1

a1 =1

Check

a1=1

a2 = (2*2-1)+1 =3+1 =4

a3 = (2*3-1)+4 =5+4 =9

a4 = (2*4-1)+9 =7+9 =16