Arithmetic sequences: The main characteristic of an arithmetic sequence is that the pattern is always the same number and is just addition and subtraction.

The formula is: Tn=T1+(n-1)(d)

T1= The first term

d= Difference

Example: In a sequence 3,8,13,18…..find T18. Where T1 is 3 and T4 is 18

1- Find the difference. We can deduce it or use this formula

d=aj-ai/j-1

aj= The biggest number

ai=Smallest number

j=Biggest position

i=Smallest position

d= 18-3/4-1= 15/3= 5

Finding T18 using the formula

T18= 3+(18-1)(5)

3+85

T18=88

Sequences: It’s a series of numbers, figures, letters that follow a determined pattern.

1,2,3,4…. the pattern is always +1

2,4,8,16,32… the pattern is x2

Also this week we did a flashback in which we remembered relations and functions, factor, and SoH, CaH, ToaH

Method of substitution

Method of elimination

https://www.desmos.com/calculator/ozjq0iydad

Slope-intercept form

We use this formula: y=mx+b

where m is the slope and b is the y intercept

example:

m=3

b=2

y=3x+2

Slope: Tells you the direction of a line and you can calculate it with the following formula:

m: y2-y1/x2-x1

m: slope

Middle point: Is the point that divides a line in 2 equal parts and it can be determined by the following formula:

P(x,y)=(x1+x2)/2 , (y1+y2)/2

Domain: It is in the independent variable (x) and it can be explained as all the possible x values that are gonna make the function work and will output real y values

Range: It is in the dependent variable (y) and are all the resulting variables of the y values after we substituting all the x values

A function is a relation between the independent and the dependent variable, where the independent variable receives only 1 partner of the dependent. If the independent receives 2 partners is not a function but the dependents can receive 2 or more.