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# Algebra/Geometric, Arithmetic Sequences

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?

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
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Algebra

Volunteer

#### Socrates

##### Expertise

Any questions on High School Algebra, College Algebra, Abstract Algebra. I can help with word problems, solving equations, trigonometry, inequalities, Gaussian Elimination, Linear Algebra, groups, fields, you name it!

##### Experience

Ph.D. in Mathematics, specialist in Algebra. I have taught High School students and college students at three state universities.

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Mathematical Association of America. American Mathematical Society.

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Regular contributions to the problems section of the American Mathematical Monthly journal.

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B.S., M.S., Ph.D.