which term of the following progression 0.004,0.02,0.1,.... is 128

Question

which term of the following progression 0.00 4010 20.1 is 128

Answer 1

It is a geometric progression with common ratio, r=5 ; and first term, a=0.004

the n^th term of a geometric progression is given by,

a_n = a(r)^n-1 

for the given question we have, a_n=128

Hence,            

128=0.004(5)^n-1 

32000=5^n-1 

Taking log with base 5 on both sides

6.445=n-1 

n=7.445

Since n is not a natural number we can conclude that 128 is not a term of the series.