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In the following examples, are the terms ("in this way", "hence", "thusly" and "as follows") synonyms sufficiently formal to be used in academic work with a sense of result?

In this way, as this process occurs...
Hence, as this process occurs...
Thusly, as this process occurs...
As follows, as this process occurs...

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    Many native speakers regard 'thusly' as a pointless synonym for 'thus', and deplore its use in serious writing or speech. Also, it is an Americanism, and is likely to be greeted with raised eyebrows outside the USA. – Michael Harvey Jan 30 at 13:36
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    There is no single standard for what is formal or not formal enough for a particular work or medium; this is something you can garner only by reading works similar to yours or asking someone with experience with it to review your work. – choster Feb 1 at 20:12
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When I completed my dissertation I would often use terms like Hence and thus (I would avoid thusly). For the sake of purely academic use, I would not use "In this way" and I would change thusly to thus. The rest would be acceptable.

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