The first floor of an ancient japanese tower has 150 steps. Each floor above has 5 fewer floors than the previous. So, the second floor has 145 steps, the third 140 etc. How many floors does the tower have if the final floor has 30 steps leading to it.
Note this is an arithmetic series problem, so we use the equation: xn = a + d(n-1).
Number of steps on the first floor is 'a', i.e. a = 150.
Difference in the number of steps on each subsequent floor is -5 because there are '5 fewer than the previous', i.e. d = -5.
We are given that the number of steps leading to the final floor is 30, hence xn = 30.
Our unknown 'n' denotes the number of floors. So rearranging the arithmetic series equation for n gives:
n = (xn - a)/d + 1.
Hence n = (30-150)/(-5) + 1 = 25. The number of floors in our temple is 25.
