What Did We Do This Week?
By: Mia Stagner
Over the course of the week, our algebra class has learned about functions, sequences, and the unsolvable questions. A function is a relation between two or more sets of numbers, in which one element of the second set is assigned to each element of the first set. One way that someone can tell if a set of ordered pairs ia a function, is if they ask themselves, for example, when X=4 what is Y? If you can only give one answer, then it's a function. An example that we went over in class, was (3,8) (4,5) (5,2) (3,4); which is not a function because 3 has more than one Y value. Another example that helped me understand functions, was (1,3) (4,7) (8,9) (9,1); which is a function, because all the X values have only one Y value. Finally, my 3rd example is (2,1) (4,3) (7,8) (9,5); which is also a function, because the domain values, have one range valves. After Mr. fegley finished teaching us about functions, he began teaching us about sequences.
In the middle of the week, we started learning about sequences. A sequence is a string of objects, like numbers, that follow in a particular pattern. In class we talked about fibonacci and arithmetic sequences. A fibonacci sequence is a series of numbers in which each number is the sum of the two preceding numbers. An example of this would be 1,1,2,3,5,8; and it is a fibonacci sequence because 1+1=2, 1+2=3, 2+3=5, 3+5=8, and if someone wanted to find the next term it would be 5+8=13. The other type of sequence we learned about was an arithmetic sequence, which is a sequence of numbers, where they all have a set difference, or constant between the terms. An example of an arithmetic sequence is 5,7,9,11,13,15; and the constant is positive 2. Mr. Fegley also taught us the equation to find a missing term; an= a1 + (n-1) d. An is what the value of the nth term. N is the nth term. Also d is the constant or common difference. A1 is the first term in the sequence. If you're given the sequence 10,20,30,40 … and you want to know when you have 250, what therm is it? To find out what it is, you plug what you know into the equation
(an= a1 + (n-1)d). So after you plug in what you know you get, 250= 10 + (n-1)10. Then you distribute the 10, so you have 250= 10 + 10n -10. After you combine like terms, you're left with 250= 10n. The last step, is to divide both sides by 10, so your final answer is n=25; and the full answer is “ when the nth term is 25, it equals 250”. Also, if you needed to find out what the 100th term in this situation was, you would need to do follow these steps. First, you would plug in what you know to the equation, so it would be an= 10 + (100-1)10. After you subtract 1 from 100, you would multiply it by 10; then you would add 10 to that, and your final answer would be “ when you have the 100th term, it is equal to 1000”. The last thing we learned this week, was about the million dollar questions.
