How to add a line to the end of a set of files without using sed command?

I understand that the SED command reads all the lines in the file before adding a required line to the end of the file.

Is there another command that adds a line to the end of files without reading the entire file....

SED is increasing the processing time as the number of lines in each of the files is high (Say 1MB).

My current command is

sed -i '$ a\'"$Last_Record" $7/$File_Name*

Last_Record --> Line to be appended
$File_Name --> Naming pattern of the Files
$7 --> Parameter for the directory location

The shell can append with >> :

for file in $7/$File_Name*
do
  echo "$Last_Record" >> "$file"
done