Respuesta :

semsee45

Answer:

Part (a)

From inspection of the diagram, the pattern is:

Step 1:      1² + 1

Step 2:    2² + 2

Step 3:    3² + 3

Let x = step number

Let y = total number of squares

Therefore, the equation that represents the relationship is:  

y = x² + x

Part (b)

x² relates to the large square made up of small squares (top part of the image of each step)

x relates to the rectangle of small squares (bottom part of the image of each step)

y is the total number of small squares in the image of each step.

The pattern is

  • 1+1
  • 4+2
  • 9+3

More simply

  • 1²+1
  • 2²+2
  • 3²+3

So for an integer n

  • y=n²+n

#b

n² is pair of boxes at top side

n is boxes underneath