A summary of the

algebra concepts

Sequences and Series

• Some sequences are arithmetic because there is a common difference between terms. We call the common difference “d”.

• You need to be able to recognize a sequence as arithmetic, find the common difference, find a particular term (50th term), find the sum of a certain amount of terms (series) and problem solve using your understanding of the concepts.

• Some sequences are geometric because there is a common ratio between terms. We call the common difference “r”.

• You need to be able to recognize a sequence as geometric, find the common ratio, find a particular term (50th term), find the sum of a certain amount of terms (series) and problem solve using your understanding of the concepts.

It is important to determine what type of sequence you

have.• 20,25,30,35,… arithmetic• 20,40,80,160,… geometric

Arithmetic Formulas

1( )2n n

nS u u

1 ( 1)nu u d n

• Remember to reason your way through problems. When finding an arithmetic series, pair up the first and last terms and multiply by how many pair you have.

• When finding a particular term, start with the first term and reason through how many times you have added the common difference.

• Remember to reason your way through problems. When finding a geometric series, the formula will be given to you. Be clear on what the “n” and “r” represent.

• When finding a particular term, start with the first term and reason through how many times you have multiplied the common ratio.

Exponentials and Logarithms

• You need to be able to solve equations with exponentials or logarithms. Be sure you are clear on how to change bases and how to check your answer.

• Many times when dealing with a logarithmic equation, if you are stuck, change it to an exponential. If you are stuck when dealing with an exponential, take the log of both sides.

• Be sure you know how to use the log properties.

It is critical that you understand

this.

lognbA b A n

Solve

316 2log log 9x x

32

22

loglog 9

log 16

xx

32

2

3

42 2

loglog 9

4

log log 9

xx

x x

1.252log 9x

9 1.252 x

1.25 92

147.033

x

x

Permutations & Combinations

• You need to know how to use the keys on your calculator for both

nrP

nrC

• Know that when dealing with permutations, the order does matter. The order does not matter when dealing with combinations.

• Be able to apply your knowledge to problem solve.

• An example would be to find the probability of making at least 3 free throws when you are a 75% shooter given 5 shots.

This represents all possibilities.

We need to focus only on the first 3 terms.

5 0 4 1 3 25 5 50 1 2

2 3 1 4 0 55 5 53 4 5

.75 .25 , .75 .25 , .75 .25 ,

.75 .25 , .75 .25 , .75 .25

C C C

C C C

1 .2373 5 .3164 .25 10 .4219 .0625

.8965

89.7%

Mathematical Induction

• The principle deals with understanding this:

• First, state the proposition to be proven• Next, show the proposition is true for

the first term.• Assume the proposition is true for the

Kth term and use it to show the proposition is true for the (k+1)th term.

• State that the (k+1)th proposition is true.

• State that the nth proposition is true.