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Question
Hi,
My math teacher gave us this problem:

Calvin and Phoebe start walking from the same point at the same time going in the same direction. Phoebe starts with a 12 inch step and increases her step by 1/2 inch each step. She goes 21 steps and stops. Calvin starts with a 36 inch step and each subsequent step is 90% of the preceding one. Respond below.

A. What kind of sequence do Phoebe's steps follow? Write the explicit form.

B. What kind of sequence does Calvin's steps follow? Write the explicit form.

C. How long is Phoebe's last step?

D. How long is Calvin's 21st step?

E. What is the domain of theses sequences?

Could you please explain and solve these? I thought I did the right thing by writing my sequences down, but my teacher marked them wrong. Here is what I got for the first 3:

A: 1/2*12n-1
B: an= -32*4n+29.16
C: 1.91687996*10^21

Thank you so much in advance,
-Sara

Answer
Phoebe's gait is an arithmetic sequence. The nth term is 12 + (n-1)/2.
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Calvin's gait is a geometric sequence. The nth term is 360.90ⁿ⁻.
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Phoebe's last step has length 12 + (21-1)/2 = 22 inches.
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Calvin's 21st step has length 360.90⁻ = 360.90⁰ ≅ 4.38 inches.
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I am not certain of the domains, sorry.

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