Answer:
associative
Step-by-step explanation:
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<h3>
Answer: < -3, 3 ></h3>
The original translation < 3, -3 > moves the figure 3 units to the right and 3 units down.
We undo this by moving 3 units left and 3 units up, which is what < -3, 3 > describes.
You can try to show this by induction:
• According to the given closed form, we have
, which agrees with the initial value <em>S</em>₁ = 1.
• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume

and

We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or

From the given recurrence, we know

so that






which is what we needed. QED