sed increment number

Question

I'd like to substitute some text with an incremental value. Considering file xx:

<outro>dfdfd</outro>
<RecordID>1</RecordID>
<outro>dfdfd</outro>
<RecordID>1</RecordID>
<outro>dfdfd</outro>
<RecordID>1</RecordID>
<outro>dfdfd</outro>

and sed command:

for n in seq 3;do sed -e 's/<RecordID>\d/<RecordID>'`echo $n`'/' xx; done

the echo $n command does not get incremented.

Tryed also:

n=1; sed -e 's/<RecordID>/<RecordID>'`echo $n ;let n=$n+1`'/g' xx

but with no success.

Considering only sed (no awk or perl) how can I have the RecordID field incremented as in:

<outro>dfdfd</outro>
<RecordID>1</RecordID>
<outro>dfdfd</outro>
<RecordID>2</RecordID>
<outro>dfdfd</outro>
<RecordID>3</RecordID>
<outro>dfdfd</outro>

Answer 1

while read line; do n=$((++n)) &&  echo $line|sed -e 's/[0-9]/'$(($n))'/' ; done < patt