Question 15836: I have a set of ordered pairs and I can see the pattern but I can't figure out the formula that relates them. This was a challenge question in my pre-algebra class.
(1,1) (2,3) (3,6) (4,10) (5,15).... I graphed it but I don't know yet how that helps me. Thanks -Iris
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! This was a challenge question in my pre-algebra class.
(1,1) (2,3) (3,6) (4,10) (5,15)....
key to such problems is to analyse the pattern...each is an ordered pair
1st numbers in the ordered pairs are 1,2,3,4,5..etc...so each increases by 1 so graph these seperately if you want .you will find a straight line ..here n th. number is n if we call these as x1,x2,x3,x4,x5...etc then xn=n ...( you can check by putting n=1,2,3 etc when you will get the first numbers in the pairs as 1,2,3,4,5..etc.. )
now 2nd nos. are 1,3,6,10,15..no constant difference or ratio is visible so try the differences between pairs of consecutive numbers..
3-1=2
6-3 =3
10-6=4
15-10=5...now this is a pattern ..if we call the 1 = y1...3=y2...6=y3...10=y4...15=y5..then
y2-y1=2
y3-y2=3
y4-y3=4
y5-y4=5
....
....
yn-y(n-1)= n...see the pattern ..check if you want as explained above
add all the above ...we get
yn-y1=2+3+4+5+...n
yn = y1+2+3+4+5+......n =1+2+3+4+5+.....n =you will learn it as equal to n(n+1)/2
hence yn =n(n+1)/2 ....check if you want as explained above
that is put n=1,2,3,4,5...etc in n(n+1)/2.. ...we get..y1,y2,y3,y4,y5...etc.as 1,3,6,10,15...respectively
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