You are correct: at end of year 1, value = 10x.
You are correct: at end of year 2, value = (10x + 10)x [note: first term is prior year end value]
So - end of year 3, first term is its prior year end value, which = (10x + 10)x
giving [(10x + 10)x + 10]x = 10x^3 + 10x^2 + 10x
Rinse and repeat.
