Question 28231: The problem gives a chart of numbers with a difference of the same number- a pattern.ie. 14-1,12-2,10-3,8-4,etc. The first numbers are variable Y, and the 2nd numbers are var.X, ie.14=Y and 1=X. HOw do I find a formula for this?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! The problem gives a chart of numbers with a difference of the same number- a pattern.ie. 14-1,12-2,10-3,8-4,etc. The first numbers are variable Y, and the 2nd numbers are var.X, ie.14=Y and 1=X. HOw do I find a formula for this?
IN SUCH PROBLEMS LOOK FOR A PATTERN...AS YOU POINTED OUT IT IS HAVING Y-X PATTERN...OK...
NOW LOOK AT NUMERS IN Y POSITION...THEY ARE
14,12,10,8 ETC....THEY ARE DECRESING BY 2 AT EVERY STEP STARTING FROM ..IT IS CALLED ARITHMATIC PROGRESSION WITH FIRST TERM AS 14 AND COMMON DIFFERENCE AS -2
SO ITS GENERAL TERM IS 14+(N-1)(-2)=14-2N+2=16-2N...YOU CAN CHECK THIS BY SUBSTITUTING N=1,2,3 ETC...TO GET 14,12,10 ETC...
SIMILARLY FOR NUMBERS IN X POSITION THE GENERAL TERM IS N...SO...
Y-X ...IS.....16-2N-N=16-3N
SO GENERAL FORMULA FOR N TH. TERM IS 16-3N.....LET US CHECK....
N=1............13
N=2............10
N=3............7...ETC...
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