Sorry, I know I just posted this, but I need to make some new changes.
Can somebody please check my work? Thanks.
1. Robin wants to create a sequence to model how much money he's saved through allowance over the weeks of the school year. In the first week, he has $40 and gains $12 each week. If we were to model this situation with a sequence, which type of sequence is more appropriate?
-Answer: arithmetic sequence
-geometric sequence
-a different type of sequence that is neither arithmetic or geometric.
2. Which recursive equation best models the situation from Question 1?
-Answer: t(n + 1) = t(n) + 12, where t(1) = 40
-t(n + 1) = t(n) • 12, where t(1) = 40
-t(n + 1) = t(n) + 40, where t(1) = 12
-t(n + 1) = t(n) + 12, where t(1) = 0
3. Emilia purchased a collectible item for $100. She thought it was a good investment, but it is starting to lose it's value! The value of the item remained at $100 for an entire year. But after, it began to follow a pattern of losing it's value by 2/3 each year. Is this situation best modeled with an arithmetic sequence or a geometric sequence?
-Geometric Sequence
-Answer: Arithmetic Sequence
-Neither
4. Which recursive equation best models the situation from Question 3?
-Answer: t(n + 1) = t(n) • 2/3, where t(1) = 100
-t(n + 1) = t(n) + 2/3, where t(1) = 100
-t(n + 1) = t(n) • 100, where t(1) = 2/3
-t(n + 1) = t(n) • 2/3, where t(1) = 66
1. correct
2. correct
3. no
4. correct
I am curious,
in #4 you correctly did show that it was geometric, since you multiplied
a term to get the next one, yet it #3 you said it was arithmetic.
Sorry, I was slightly confused on #3 because we never really went over a word problem that was decreasing with sequences. I accidentally saw 2/3 as a whole number (I don't know why). My first answer for #3 was Geometric, but I think I over-thought my answer and changed to arithmetic.
1. The situation described in question 1 involves Robin saving a certain amount of money each week. Since he gains a fixed amount of $12 each week, this can be modeled by an arithmetic sequence. In an arithmetic sequence, each term is obtained by adding a common difference to the previous term.
To determine if a sequence is arithmetic, we can check if the difference between consecutive terms is constant. In this case, the difference is $12, which remains the same throughout the sequence. Therefore, the appropriate type of sequence for this situation is an arithmetic sequence.
2. The recursive equation is used to define each term in the sequence based on the previous term(s). In question 1, Robin's savings follow the arithmetic sequence with a first term of $40 and a common difference of $12. To find the recursive equation, we need to express the next term (t(n + 1)) in terms of the current term (t(n)).
Among the given options, the equation t(n + 1) = t(n) + 12, where t(1) = 40, best models the situation. This equation states that each term (starting from the second term) is obtained by adding 12 to the previous term.
3. The situation described in question 3 involves the value of a collectible item decreasing each year. Since the value is decreasing by a fixed ratio (2/3), this can be modeled by a geometric sequence. In a geometric sequence, each term is obtained by multiplying the previous term by a common ratio.
To determine if a sequence is geometric, we can check if the ratio between consecutive terms is constant. In this case, the ratio is 2/3, which remains the same throughout the sequence. Therefore, the appropriate type of sequence for this situation is a geometric sequence.
4. Similarly, the recursive equation for the geometric sequence described in question 3 can be found by expressing the next term (t(n + 1)) in terms of the current term (t(n)). Among the given options, the equation t(n + 1) = t(n) * 2/3, where t(1) = 100, best models the situation. This equation states that each term (starting from the second term) is obtained by multiplying the previous term by 2/3.