x| 1| 2| 3| 4| 5| 6| 7| -|--|--|--|--|--|--|--| y| 2| 5| 6|11|12|19|20| (1,2), (2,5), (3,6), (4,11), (5,12), (6,19), (7,20) Taking the points where x is odd: We find the quadratic equation through (1,2), (3,6), (5,12), (7,20) by substituting three of those points in y = ax˛+bx+cSimilar we take the points where x is even and find the quadratic equation through (2,5), (4,11), (6,19) where x is even We compare the two quadratic equations: When x is odd the coefficient of x in the parentheses is 4, and when x is even the coefficient of x in the parentheses is 6 The average of 4 and 6 is 5 4 = 5-1 and 6 = 5+1 So the coefficient of x is 5+(-1)x in either case --- When x is odd, the constant term in the parentheses is 3, and when x is even, the constant term in the parentheses is 4 The average of 3 and 4 is 7/2 3 = 7/2-1/2 and 4 = 7/2+1/2 the constant term in the parentheses is 7/2+1/2(-1)x in either case So the general term is which simplifies to In sequence notation we replace y by an and x by n Edwin