Starting with any rectangle, we can create a new and larger rectangle by attaching a square to the longer side. For example, if we start with a 2x5 rectangle, we would attach a 5x5 square to the 5 sides of the original rectangle to obtain a 5x7 sided rectangle; we could then proceed recursively attaching a 7x7 square to this rectangle to obtain a 7x12 sided rectangle. a. Create a sequence of rectangles using this rule starting with a 1x2 rectangle. Then let a_n the sequence of perimeters of these rectangles starting with a0=1+2+1+2=6a0=1+2+1+2=6 b. Do the same for the sequence starting with a 1x3 rectangle. c. Find recursive formulas for both sequences (don't forget the initial conditions) d. Are the sequences arithmetic or geometric? Are they close?
Starting with any rectangle, we can create a new and larger rectangle by attaching a square to the longer side. For example, if we start with a 2x5 rectangle, we would attach a 5x5 square to the 5 sides of the original rectangle to obtain a 5x7 sided rectangle; we could then proceed recursively attaching a 7x7 square to this rectangle to obtain a 7x12 sided rectangle.
a. Create a sequence of rectangles using this rule starting with a 1x2 rectangle. Then let a_n the sequence of perimeters of these rectangles starting with a0=1+2+1+2=6a0=1+2+1+2=6
b. Do the same for the sequence starting with a 1x3 rectangle.
c. Find recursive formulas for both sequences (don't forget the initial conditions)
d. Are the sequences arithmetic or geometric? Are they close?
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