Geometric Sequences

Monday in class we talked about geometric sequences, where there is a constant ratio between terms. We learned the equation and worked some practice problems, as usual. We also discussed finding the sum of terms in a geometric sequences, which usually has to be done on a calculator.

Arithmetic Sequence

new formula for linear functions, new term Arithmetic Sequence 

d is the constant difference between the terms 

can find the formula from a sequence, can also find a sequence from a formula 

lots of examples 

Sequences, Recursion, Sigma

Today we practiced sequences, recursive notation, and played with summation/sigma. The new things were mainly the latter 2. Recursive notation is a way of writing a sequence in such a way that the method calls itself. Recursive notation requires 2 things: An defined by a change in An-1 and a start point, a value for A1. Sigma notation is used when talking about adding everything up in a sequence. You put the lower limit on the bottom and the upper limit on the top. Next to the sigma, write the function that you will call each time to produce the next number in the sequence and that number will get added to the previous number until the upper liimit has been reached. You can use the calculator if the numbers get messy. 2nd -> Stat -> math for sum and -> ops for seq and then type in the function, variable being used, start value, end value

Sequences

Yesterday's class involved an introduction to sequences - namely, continuing a few sequences and writing formulae for them.

Square Roots of Complex Numbers

In class, we learned how to find the square roots of complex numbers.  We also learned how to take the cube and fourth roots of complex numbers by solving some sample problems.  

Complex Number Arithmetic

Today in class, we learned about complex number arithmetic. We learned a new notation involving cis instead of (cos + i sin). Also, we learned how to multiply and divide complex numbers. Finally, we learned Moivre's Theorem when dealing with powers and complex numbers.

Polar Graphing

Today in class we learned about cardioid and limacon types of polar graphs and we graphed examples on a worksheet. We talked about how petals of a rose curve are on the axis when there is a cosine equation. We also learned that limacon curves have an inner loop, they are dimpled, and are convex.

Polar Graphing

Today in class, we learned how to graph polar equations. We started by plotting points on polar graph paper. We graphed two different examples, a circle and a rose curve. Then, we studied how different parts of the polar equation affect the graph.