The common difference is -x/2. Therefore we have the sequence continue as:
2x, 3x/2, x, x/2, 0, -x/2, -x, -3x/2, -2x, -5x/2......etc.
And -5x/2 being the 10th term.
We have:
-5x/2 = 2x + (N - 1)* -x/2
Solve for N:
-(5 x)/2 = 2 x - 1/2 x (N - 1)
-(5 x)/2 = 2 x - 1/2 (N - 1) x is equivalent to 2 x - 1/2 (N - 1) x = -(5 x)/2:
2 x - 1/2 x (N - 1) = -(5 x)/2
Expand out terms of the left hand side:
(5 x)/2 - (N x)/2 = -(5 x)/2
Subtract (5 x)/2 from both sides:
-(N x)/2 = -5 x
Divide both sides by -x/2:
Answer: | N = 10 which is the 10th term of your sequence.
