Hello Aniruddha
While solving these type of questions,
We want to write the terms as (10 - 1), (100 - 1), (1000 - 1) ....
So that is why we take 7 common,
and then multiply and divide by 9.
So that we get numbers as
9, 99, 999..
which we can write as
(10 - 1), (100 - 1), (1000 - 1), ....