1. After returning from a knee injury, your trainer tells you to return to your running program slowly. She suggests running for 60 minutes total for the first week. Each week thereafter, she suggests that you increase that time by 6 minutes each week. What type of sequence best models this scenario?

-Arithmetic Sequences
-Geometric Sequence
-Neither

2. Which sequence best models the scenario from Question 1?
-60, 54, 48, 42, ...
-60, 66, 72, 78, ...
-60, 360, 2160, ...
-54, 60, 66, 72, ...

3. Write a recursive equation to model the sequence from question 2
-t(n + 1) = t(n) + 6, t(1) = 0
-t(n) = 6n + 54
-t(n + 1) = t(n) + 6
-t(n + 1) = t(n) + 6, t(1) = 60

4. A professional basketball player signs a contract with a beginning salary of $3,000,000 for the first year and an annual increase of 4% per year. That is, beginning in year 2, the athlete's salary will be 1.04 times what it was in the previous year. What type of sequence best models the scenario?
-Geometric Sequence
-Neither
-Arithmetic Sequence
-No answer text provided.

5. Which sequence best models the scenario from question 4.
-3,000,000 , 120,000 , 4,800 , 192 , ...
-3,000,000 , 3,004,000 , 3,008,000, ...
-3,000,000 , 3,000,004 , 3,000,008, ...
-3,000,000 , 3,120,000 , 3,444,800, ...

6. Write a recursive equation to model the scenario and sequence from questions 4 and 5.
-t(n + 1) = 1.04•t(n)
-t(n) = 3,000,000(1.04)^n
-t(n + 1) = 1.04•t(n) , t(1) = 3,000,000
-t(n + 1) = t(n) + 1.04 , t(1) = 3,000,000

6 answers

arithmetic sequences involve adding the same amount to each term
geometric sequences involve multiplying by the same amount

So now, what are your thoughts here?

1. Arithmetic

2. The second answer

what's a recursive equation?

a recursive equation tells how to produce the next term in the sequence, given the previous term. For #4, you

are supposed to keep multiplying by 1.04. So the sequence is hgenerated by the recursion

A_1 = 3,000,000
A_n+1 = A_n * 1.04

So the sequence is
3,000,000 , 3,120,000 , 3,444,800, ...

thanks