Why is this usefull in life?
Does anything you do remind you of AP?
Does anything around you remind you of AP?
What are the important things in a series or progression?
Things that are changing must have a starting position.
Your age had a starting point. Your height had a starting point.
Everything you know bankaccount, friendship, a movie, etc
Now if it is changing, then it means by what amount it is changing?
If these amount is the same then we have an AP.
If you need the 7th position or term then
- out of the 7 terms, the 1st must be the start
- then the rest will be the consistant changes. In this case it will be (7-1) which is 6
- So the 7th term 1st + (7 -1) change i.e. a + (n-1)d is the nth term
Give some examples of terms e.g. 27th term, 32nd term, etc
A progression is somthing in which a constant is added to each term in order to obtain the next term;
ReplyDeleteit is useful because is makes identifying trends easier and it give us and idea in predicting outcomes of things based on statistics.
AP= The thickness of a roll of paper where the first term is the diameter of the core of the roll and twice the thickness of the paper is the common difference. & Suppose you were building a picket fence on a regularly sloping path with the top of the pickets being horizontal. The lengths of the pickets will form an AP.
eg. is i need the 20th term
out out of 20 terms, 1st will be my start.
rest wil have consistant changes eg (20-1=19)
therefore the 20th term 1st+(20-1)change
In mathematics, an arithmetic progression (A.P.) or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, 13... is an arithmetic progression with common difference 2.
ReplyDeleteRemember ap is addition and gp is multiplication
i found this example of an ap progession....
ReplyDeleteOne example I had thought of which kinda works is the score in a basketball game. The teams score increases by 2. The only fault with this example is that you can score a 3 pointer or foul shot worth 1 point. a=0 and d-2
Scoring in Hockey is an arithmetic sequence though with a=0 and d=1
Arithmetic Progressions (A. P.)
ReplyDeleteThe sequence a , (a +d ), (a +2d ), (a +3d ), (a +4d ), . . . is called an arithmetic progression.
' a ' is the first term and
' d ' is the common difference of the A.P.
The nth term of the A.P. is a + ( n-1)d
The sum of n terms of the A.P. is =
n/2[ 2a + (n - 1 ) d ]
Geometric Progression (G.P)
ReplyDeleteThe sequence a, (a*r),(a*r*r), (a*r*r*r).....
is equivalent to a, ar, ar^2, ar^3.....
'a' is the first term
'r' is the common ratio of the G.P.
The nth term of the G.P. is ar^(n-1)
The sum of n terms of the G.P. is
=sn= a(r^(n-1)-1)/r-1
A series or progression is a sequence or pattern being formed when you move from one position to the other by addition.
ReplyDeleteThe important things in a series or progression are:
ReplyDeletethe first term (a)
the last term
the number of terms or elements (n)
the common difference (d)
example of an AP
ReplyDeleteif a someone collects pens and starts on the 1st day with 5.
And everyday he adds 4 more to his collection.
How many pens would he have at the end of the day?
a=5
d=4
n=28
last term = a+(n-1)d
= 5+(28-1)4
= 5+(27)4
= 113
therefore by the end of 28 days he would now have 113 pens in his collection.
Series or Progression involves addition
ReplyDeletegood example there lykke but i think you mean "at the end of 28 days in stead of the day."
ReplyDeletei dunno if this would help you darky but " Arithmetic Progressions involve the addition of a constant term until the nth term. Geometric Progression involves multiplication where you have a common ratio (r).
ReplyDelete