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
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
1. The scenario in question 1 involves increasing the running time by a fixed amount each week. This type of sequence is called an Arithmetic Sequence.
2. Looking at the options provided, the sequence that best models the scenario is 60, 66, 72, 78, ... Each term is obtained by adding 6 to the previous term.
3. To write a recursive equation for this sequence, we can use the formula t(n + 1) = t(n) + 6, where t(1) = 60. This equation states that each term in the sequence is obtained by adding 6 to the previous term.
4. The scenario in question 4 involves a salary that increases by a certain percentage each year. This type of sequence is called a Geometric Sequence.
5. Looking at the options provided, the sequence that best models the scenario is 3,000,000 , 3,004,000 , 3,008,000, ... Each term is obtained by multiplying the previous term by 1.04.
6. To write a recursive equation for this sequence, we can use the formula t(n + 1) = 1.04•t(n), where t(1) = 3,000,000. This equation states that each term in the sequence is obtained by multiplying the previous term by 1.04.