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Sagot :
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
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