# Maths Revision: A2: Sequences and linear graphs

- Created by: daniella
- Created on: 02-06-13 10:24

## A2.1: Generating sequances

**What is an example of a general term?**

**T**n = **n**2 **+ 3**

**What is the nth term?**

if it the term is the first in the sequence its nth term is 1, second term is 2 etc. etc. etc.

**What tells you which term it is?**

**T**n- whatever the small n is, is the number that the term is in the sequance

**What is a diverging sequance?**

if every term is bigger than the last (it is increasing)

**What is an oscillating sequance?**

if the terms alternate between positive and negative

## A2.1: Generating sequances

**How can you tell if an oscillating sequance is diverging or not?**

if the difference between the terms is increasing

**Give an example of this**

2, -4, 6, -8, 10, -12

**What is a converging sequance?**

when each term is smaller than the one before, **but will never be will never be equal to 0.** get closer and closer to 0.

**Give an example of this**

1, 1/2, 1/3, 1/4, 1/5

## A2.1: Generating sequances

**What to look for in a sequance**

- does it
**add by the same number?** - does it
**add by more each time?** - does it
**minus by the same number**? - does it
**minus by more each time**? - does it
**multiply by the same number**? - does it
**devide by the same number**? - does it
**add the two previous terms**? - is it a
**pattern sequance?** - is it the
**previous number squared**?

**How can you put this into a table if they havn't already made a table**

put pattern number in the first column and number of ---------

## A2.2: The nth term of a linear sequence

**How to figure out the nth term rules:**

- Figure out the difference between every term... this is the number before n
- Figure out the first term minus the difference (if its - number it would be for example 2n -3)
**How to find a terms position (n) in a sequance:**

1.) write for example if the term was 23 that you had to figure out the position of and the rule was 3n- 2 **you would write 3n-2=23**

2.) cancel down so that you have only n on one side and a number on the other

3.) the number is the position of n

4.) if n is not a whole number and is a decimal it is not in the sequance

**What is an arithmetic and linear sequence**?

when the difference between each term is the same every time

## A2.2: Putting the nth term into a table

**first row: term number (n)**

**second row:** **_n**

the _ is the common difference

**third row****: term**

## A2.3: Line graphs

**What is the equation for straight line graphs:**

y = mx + c

**What does m stand for?**

the gradient

**What does c stand for?**

the y-intercept

**What tells you where a line would slop upwards or downwards?**

m

**How ?**

if m is a positive number then the gradient and line slopes upwards. if m is a negative number then the gradient and line slopes downwards.

## A2.3: Line graphs

**vertical line:**

you write x = _ (the _ being whatever x always equals)

**horisantal line:**

you write y = _ (the _ being whatever y always equals)

## A2.3: Line graphs

**what does y = x look like?**

a diagonal line where the y intercept is 1 and the gradient is also 1. it has a positive gradient therefore the line slopes upwards.

**what does y = -x look like?**

a diagonal line where the y intercept is 1 and the gradient is also 1. it has a positive gradient therefore the line slopes downwards.

**what do sloping lines that cross at the y intercept have the equation of?**

y=mx

**what do you write if m = 1/-1**

y = x + c

y = -x + c

## A2.3: Line graphs

**Cancelling down**

- when multiplying fractions by a significant figure, write write sf. as sf./1
- EXAMPLE
- to get rid of a divide, multiply both sides by whatever is devided (or on the bottom line)
- you can't cancel down things on opposite sides of the equals sign
- when x or / you must x or /
**everything**on the opposite side

**finding where two lines cross/meet**

- get at least on of the two equations to y=mx+c
- wherever you see y in the harder equation, replace it with write whatever y = in the easy one
- simplify to find what x equals, so y is before the equals sign and x is after the equals sign
- subtitute what x is into the easy equation to find y

IT DOESN'T ACTUALLY HAVE TO START WITH FINDING Y.

## A2.4: Finding the equation of a straight line

**How to find out the gradient of a line:**

change in the vertical direction / change in the horisontal direction

**finding what to equation of a line is when give two points in it (that would join to give the line)**

- figure out the change in the two y figures in the (x,y)'s (lets call this Z)
- figure out the change in the two x figures in the (x,y)'s (lets call this Y)
- figure out Z/Y
- substitute the x and y from the first (x,y) and m into the equation y= mx+C (LETS CALL THIS A)
- look at A, and rearange so you get c= _____

**what changes in perpendicular lines?**

the y intercept (c)

## A2.5: Perpendicular Lines

- Change
**M**by making it a**negative**number and make it the**RECIPRICAL** - The rest of the equation you keep the same

EXAMPLE:

If M equals 4/3 turn it into -3/4

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