seq 1 10 | awk '{s+=$1} END {print s}'

awk processes input line by line: the pattern {s+=$1} accumulates the first field of every line into s, and the special END block prints the total after the last line. The pipe symbol (|) feeds seq's output into awk's input. This is the canonical awk accumulator pattern. It works on any whitespace-separated stream, not just seq output.