I was doing a problem on Arithmetic progression where I have to find number of terms those are multiples of 7 between 400 & 500.

I found that value of a term which is multiple of 7 can be generailzed by:
400+(7n-1) [where n=1,2,3...][constructed this by using firs multiple 406]

and no of terms was found by: 7n = 100 [since total 100 terms between 400&500]

so n= 14 (approx.)

This can also be done:
400+(7n-1) <500
by calculating n<14.43 which can be said n=14

I wanna know are these methods right? Is there any general formula of multiples of any number??

I don't know about any formula, but what you have done in this case is correct and has given you the correct answer.