Question

good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.

Answer 1

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

Answer 2

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.