**The solution** for question (i):

**The solution** for question (ii):

25^{(n-1)} + 100= 5^{2n-1}

given equation is:

let 5^{2n-1} = t , therefore, the above equation becomes:

t+100=5t

5t-t=100

4t=100

t=100/4=25

hence, 5^{2n-2}=25=5^{2}

Since the base is same comparing the exponents:

2n-2=2

2n=2+2=4

n=4/2 = 2

**n=2**