A mutation occurs in an original DNA template that changes the DNA, changes the RNA, but does not change the protein sequence. What kind of mutation is this. and what would be the consequence of this original change?

The changes that do not affect the function of a protein are called silent mutations.

Explanation:

As given here as a mutation occurs in an original DNA template that changes the DNA, by transcription this mutation passes into RNA and changes the RNA, but it does not change the protein sequence, it means that this mutation could be silent mutation.

Silent mutation is the mutation which cause the change of a base in that, after the mutation the codon codes for the same amino acid, or the amino acid which do no cause any change in the protein, hence these changes do not affect the function of a protein.