Weekly Reflection 11-16-18
Arithmetic and Geometric Sequences:
I will be able to understand arithmetic series and sequence. I will be able to understand geometric series and sequence.
Example of arithmetic sequence:
-9,-2,5,12,___,___,___,___
a(n)=a(1) + (n-1)d
I do not know what my end term[a(1)] is so that is what I am looking for. I do know what my first term [a(1)] is, it is -9, I have 8 terms [n] and I can find my common difference by subtracting -2 from -9. which is 7. To solve all I need to do is add 7 to 12 then to that number and so on until I have all the terms I need.12+7=19, 19+7=26, 26+7= 3, and 33+7= 40. Now that I have my four terms I can add them to my series.
Solution: -9,-2,5,12,19,26,33,40
Example of geometric sequence:
Find two geometric means between -2 and 54
-2, __, __, 54
a(n)=a(1)*r^(n-1)
I do know what my end term is, it is 54, my first term is -2, I do not know what the common ratio is I have to solve to find it, but I do know how many terms there are, there are 4. After I plug all of the values I have: 54=-2*r^(4-1) The first thing to do is divide -2 to both sides, next solve 4-1=3, then square root both sides by 3 and end with -3 = r. Now that I know my common ratio I can multiply -2 by -3 and get 6. Then multiply 6 *-3= -18 and just to check to make sure -3 is correct multiply -18 * -3 and get 54.
My Solution: -2,6,-18,54
One mistake I made was trying to figure out which Geometric sum equation to use. I was unsure whether to use the finite or infinite series. I overcame this misconception when I asked one of my classmates to explain further and they told me what situations called for which equation.
Answer EQ- How do you determine domain and range? (Power function)
You can determine the range by looking at how the graph goes from the bottom to the top of the graph and you can determine the domain by looking at what the graph does from left to right of the graph.
How do I find a given term in an arithmetic or geometric sequence? How do I find the sum of an arithmetic or geometric series.
You can find a given term by plugging in the term number you need into the "n" of either equation, you can find the sum by using the equation S(n)=n/2(a(1) +a(n)) for arithmetic or S(n)=[ a(1) (1-r^n)]/1-r for geometric finite series or S=a(1)/1-r geometric infinite series
I will be able to understand arithmetic series and sequence. I will be able to understand geometric series and sequence.
Example of arithmetic sequence:
-9,-2,5,12,___,___,___,___
a(n)=a(1) + (n-1)d
I do not know what my end term[a(1)] is so that is what I am looking for. I do know what my first term [a(1)] is, it is -9, I have 8 terms [n] and I can find my common difference by subtracting -2 from -9. which is 7. To solve all I need to do is add 7 to 12 then to that number and so on until I have all the terms I need.12+7=19, 19+7=26, 26+7= 3, and 33+7= 40. Now that I have my four terms I can add them to my series.
Solution: -9,-2,5,12,19,26,33,40
Example of geometric sequence:
Find two geometric means between -2 and 54
-2, __, __, 54
a(n)=a(1)*r^(n-1)
I do know what my end term is, it is 54, my first term is -2, I do not know what the common ratio is I have to solve to find it, but I do know how many terms there are, there are 4. After I plug all of the values I have: 54=-2*r^(4-1) The first thing to do is divide -2 to both sides, next solve 4-1=3, then square root both sides by 3 and end with -3 = r. Now that I know my common ratio I can multiply -2 by -3 and get 6. Then multiply 6 *-3= -18 and just to check to make sure -3 is correct multiply -18 * -3 and get 54.
My Solution: -2,6,-18,54
One mistake I made was trying to figure out which Geometric sum equation to use. I was unsure whether to use the finite or infinite series. I overcame this misconception when I asked one of my classmates to explain further and they told me what situations called for which equation.
Answer EQ- How do you determine domain and range? (Power function)
You can determine the range by looking at how the graph goes from the bottom to the top of the graph and you can determine the domain by looking at what the graph does from left to right of the graph.
How do I find a given term in an arithmetic or geometric sequence? How do I find the sum of an arithmetic or geometric series.
You can find a given term by plugging in the term number you need into the "n" of either equation, you can find the sum by using the equation S(n)=n/2(a(1) +a(n)) for arithmetic or S(n)=[ a(1) (1-r^n)]/1-r for geometric finite series or S=a(1)/1-r geometric infinite series
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