Arithmatic Sequences

Today in class we went over functions, and learned about arithmetic sequences and inductive reasoning.

A function is a relation between a number in the range(the f(x) or y) and the domain(the x). You use the numbers to plot points on a graph. For example:
If you had the function f(x)=2.5x and -8, 5, and 0 as x values, you would substitute in the x values to get the y values.
f(x)=2.5(-8) f(x)=2.5(5) f(x)=2.5(o)
f(x)=-20 f(x)=12.5 f(x)=0

This would mean that the points (-8, -20) (5, 12.5) and (o, o) would be graphed as the function f(x)=2.5x.

Also today learned about inductive reasoning. It is when you recognize a pattern, and can continue it. One example is the numbers 1, 4, 16, 64. You recognize the pattern is times 4, and can continue it(256, 1024).

Last we learned about sequences. A sequence is a number pattern. It is made up of terms. An arithmetic sequence is any sequence where a fixed amount is added to the term before it. Example:
19, 23, 27, 31, 34
The fixed amount added is 4.
Even though it is called an arithmetic sequence, the numbers can go up OR down, as you can add negative numbers.

In the sequence below, the number added, or the common difference, is -8.
42, 34, 26, 18, 10