Monthly Archives: February 2018

Week 3-Radicals

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This week, we started working with radicals. This week, I wanted to show how one would simplify radicals. I feel like this will help myself when studying for the final.

Ex. \sqrt{27}

when simplifying radicals, you want to look at the number you are using, in this case, 27, and finding what perfect square goes into it. For 27, it is 9 because 9×3=27.

We can square the 9 and but it outside the root and keep the other 3 on the inside because it cannot be squared. The simplified version of \sqrt{27}  is 3\sqrt{3}

Week 2- Geometric Series

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This week, we started by learning how to find a common ratio for geometric series’. Geometric series are when one number is multiplied by the same number each time.

Ex. 3, 9, 27

To find the common ratio (r.) We have to divide the first term by the second term. \frac{9}{3} = 3

`This means that the common ratio is now 3. When we multiply each term by 3, the geometric series continues correctly.

 

Week 1- Arithmetic Sequences

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This week, we worked with arithmetic sequences.

2,4,6,8,10…

Each of the numbers above are considered terms. The number 2 is considered t_1

Part 1:

When finding a term, we use the formula: t_n = t_1 + (n-1)d  (d represents difference between terms.)

For finding term 50, we will use this formula.

t_{50} = 2 + (50-1)2

t_{50} = 2 + 98

t_{50} = 100

 

Part 2:

When finding the sum of all terms, we use the formula: s_{50} = \frac {n}{2} + ( t_1 + t_n )

I will be using the same sequence from above to find the sum.

s_{50} = \frac {50}{2} + ( 2 + 50)

s_{50} = 25+ 52

s_{50} = 77