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When using participle consturction for describing sequential event such as,

ex. He projected a dot on the wall and asked subjects to indicate the light's trajectory.

as long as I know, the underlined part can be reduced into "asking subjects to indicate...".

And if I want to emphasize the sequence I have an option to write "and asking subject to indicate.."

However, the grammar book(by Korean authors) says "and asking subject to indicate.." is ungrammatical.

I just cannot find out why it is wrong. Please help!

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cho7712And if I want to emphasize the sequence I have an option to write "and asking subject to indicate.

Sorry. You do not have that option.

cho7712However, the grammar book(by Korean authors) says "and asking subject to indicate.." is ungrammatical.

Correct. It is ungrammatical.

cho7712[He projected a dot on the wall]finite,
[asking subjects to indicate the light's trajectory]non-finite.
I just cannot find out why it is wrong.

You can't join a finite clause to a non-finite clause with a coordinating conjunction (e.g., and). You need two equivalent structures if you want to connect them with 'and'.

CJ

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You can't join a finite clause to a non-finite clause with a coordinating conjunction (e.g., and). You need two equivalent structures if you want to connect them with 'and'.

Thank you for the answer. Then, without 'and', is "asking subjects to indicate..." a correct participle phrase?

cho7712Then, without 'and', is "asking subjects to indicate..." a correct participle phrase?

Yes. Some people say "participle"; some people say "participial". Some people call it a phrase; some people call it a clause.

CJ