In every language, there is a form of enumeration, for example, when you want to list associated or related items. Since first, second, and third as well operate in a grammatical way as well as adjectives and adverbs, you may find that including “-ly” is unnecessary. Technically, that means that you will be able to go as many levels down the ladder as you like. In other words, you will be allowed to go down: thirdly, fourthly, fifthly, and so forth.
Hence, to use the “-ly” suffix in firstly, secondly is of no real importance. Nevertheless, we do use it in everyday conversation. They are regarded as more “polite” whenever the suffix “-ly” is added, unlike ordinal adverbs without the suffix.
Am I supposed to use “firstly” and “secondly”?
There is nothing improper in using “firstly” or “secondly” to enumerate your points. Likewise, it is by no means incorrect to say the more straightforward "first,” "second,” and so forth.
Look at the following example to illustrate the point:
There are several reasons for me to apply for the new job. Firstly, I would like to take up a new challenge. Secondly, I feel I would fit well into the company, and thirdly, it is much closer than my previous job.
For me, there are several reasons why I don’t want to move away from here. First, I would like to stay with my family. Second, I know my way around here, and know all the corners, and third, I don't have the money to pay for a move right now.
What does “secondly” mean?
The adverb secondly has the same meaning as the word second. The word secondly is usually used when characterizing the second of two or more types of information.
The same applies to “third” and “thirdly”
As you can see, the sentence’s meaning does not change, and both have their justification. Even if there are, of course, reasons why one is preferred to the other.
In most cases, you tend to use second before secondly, and third before thirdly, and so on. So if you want to be on the safe side when you’re talking to someone or writing an essay, just follow this rule, and you’ll stay on the right track.