Downloading multiple SRA files from several SRA accession IDs does not work
First of all, the brace expansion you tried to use isn't valid. While bash can expand {1..3} to 1 2 3, it has no way of knowing how to expand {SRR1002678..SRR1184123}:

$ echo {1..3}
1 2 3
$ echo {SRR1002678..SRR1184123}
{SRR1002678..SRR1184123}


Perhaps you meant SRR{1002678..1184123}? But there's no need for this, you already have the accessions in a file and can read that. I see that the FTP server you are accessing has organized the data like this:

sra/sra-instant/reads/ByRun/sra/SRR/SRRNNN/SRRNNNXXXX/SRRNNNXXXX.sra


Where NNN are the 1st three digits of the accession. So, for example, the file for accession SRR1002678 is at:

ftp://ftp.ncbi.nlm.nih.gov/sra/sra-instant/reads/ByRun/sra/SRR/SRR118/SRR1181152/SRR1181152.sra


With this in mind, you can write a little script that extracts the URL from each accession:

while read i; do 
    n=$(echo "$i" | sed -E 's/(SRR...).*/\1/'); 
    wget ftp://ftp.ncbi.nlm.nih.gov/sra/sra-instant/reads/ByRun/sra/SRR/$n/$i/$i.sra
done &lt; SRR.txt


The only trick is the sed command which simply looks for SRR and the three next characters and removes everything else on the line (it "captures" the found pattern and then replaces the line with what was captured (\1)).