This is another interesting maths sequence puzzle:

When x = 1, y = 1, when x= 2, y = -1, when x = 3, y = 1,

a) if when x = 4, y = -1, what formula gives the nth term?

b) if when x = 4, y = 3, what formula gives the nth term?

Answer below in white text (highlight to see)

a) This is a nice puzzle when studying periodic graphs. Hopefully it should be clear that this is a periodic function – and so can be modelled with either sine or cosine graphs.

One possibility would be cos((n-1)pi)

b) This fits well when studying the absolute function – and transformations of graphs. Plotting the first 3 points, we can see they fit a transformed absolute value function – stretched by a factor of 2, and translated by (2,-1). So the function 2abs(x-2) -1 fits the points given.