The 1025th term of the sequence1, 22, 4444, 88888888, ..... is

1st of all let's see the no. of  repetitions  (peculiar case ;digits) in each term

they are as follows :

1,2,4,8 and so on.....

this clearly makes a g.p.

so now the 1025 th term has 2^1024 repititions

and now removing the repititions we see the series as :

1,2,4,8.... and so on 

this also makes a g.p.

so the 1025 th term is 2^1024 in this series

so the final ans. is 2^1024 repeated 2^1024 times....

an easy explaination is that

1 is repeated 1 time , 2 is repeated 2 time, 4 is repeated 4 times and so on....

pls. approve the ans.

Approved