Week 4 – radicals

This week in Math I learned how to add radicals.

Ex.  \sqrt{20}+6\sqrt5

We must simplify the radicals first.

=\sqrt{4*5}

Because we know the \sqrt4=2, we can move it to the outside of the radical.

=2\sqrt5

This is now the simplified version of \sqrt{20}

now we have 2\sqrt5+6\sqrt5

Because we have the same number inside the radical we can just add the coefficients.

So our final answer would be 8\sqrt5

Week 3-Absolute Value

This week we learned about absolute values.  an absolute value is the principal square root of the square of a number.

Ex. \mid{-2}\mid=2

This is the case because \sqrt{(-2)^2}=\sqrt4=2

So, a simpler way of defining an absolute value is to say that it is simply the number, disregarding its sign (positive or negative.)

Week 2 – geometric sequence

This week in Math we learned about geometric sequences.  A geometric sequence is a sequence of numbers where you multiply each number of the sequence by a set number called the common ratio (r) to get the next number.

Ex. 5, 10, 20, 40 …

in this case r=2 because 10/5=2 and also 40/20=2

to find any term in a geometric sequence we use this formula: t_n=a*r^{(n-1)}

So if we wanted to find t_{12} we would use that formula.

t_{12}=5*2^{11}

Therefore, t_{12}=10240.