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Algebra/Geometric, Arithmetic Sequences

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Question
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 does 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 these sequences?

Answer
A )

Arithmetic

12 , 12.5 , 13 , 13.5 ,14 ,14.5 ....

Length of the nth step is 12+(n-1)(.5)


B)

Geometric


36 , (.9)(36) , (.9)(.9)(36) , (.9)(.9)(.9)(36) ,....

Length of the nth step is (36)(.9)^(n-1)



C)

12 + (21-1)(.5) = 12 + 10 = 22




D)

(36)(.9)^20 = 4.3768  

Algebra

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