1 1 ---> Line 1 1 3/2 1 -----> row 2 1 6/4 6/4 1---------> row 3 1 10/7 10/6 10/

Question

1 1 ---> Line 1

1 3/2 1 -----> row 2

1 6/4 6/4 1---------> row 3

1 10/7 10/6 10/7 1-------------->row 4

1 15/11 15/9 15/9 15/11 1 .
.


I need to find a general FORMULA or the "nth term" to find each term of each row or line .... I know how to find it by calculation but i need is the Formula so i can use it to find ALL the terms... I NEDD THE nth FORMULA AND THE EXPLANATION OF WHY I GET TO THAT FINAL FORMULA!!! THANK YOU. (the formula needs to work for every number- from 3/2 to infinite )





* Also, I need to find how to write this formula ( im gonna write it as words)
(Number of the Row) (by) (number of terms between the 1's in that row) "-" minus ( the number that we substract)---- In gonna show that number in examples, and thos are found by the triangular numbers

FOR EXAMPLE: i want to know the numerator of the row 5
so, 5(4)= 20-5= 15
6(5)= 30-9= 21
7(6) = 42-14=28 THoSe RESULTS ARE ONLY THE NUMERATORS OF EACH ROW.
^
^
and these numbers are found by the triangular numbers because we add 4 to the 5 so we get 9, we add 6 to the 9 to get 14 and SO ON....

SO WHAT I NEED IS HOW TO WRITE THAT "WRITTEN FORMULA" IN LETTERS , FOR THE nth TERM.. Thank you!!




THANK YOU FOR THE HELP.... I NEED IT SO MUCH!!!! ;)

Explanation / Answer

basically it consists of two sequences
(1.)numerator of second and second last term
3,6,10,15 etc.
n th term=1+2+3+4+5+.....+n=(n+1)*(n)/2
as for the second row n =2
(2.)denominator of second and second last term
2,4,7,11 etc
n th term=(1+2+3+4+...+n)-(n-1)=n*(n+1)/2 -(n-1)=(n2-n+2)/2

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