Problem:

Cells in the range B2:M2 contain numerical values, and the row above contains matching serial numbers.
We want to subdivide the values into batches of three and calculate the sum of each batch.
Solution 1:

Use the SUM and INDEX functions as shown in the following formula:
=SUM(INDEX($B$2:$M$2,3*A6-2):INDEX($B$2:$M$2,3*A6))

Solution 2:

Use the SUM and OFFSET functions as shown in the following formula:
=SUM(OFFSET($B$2:$D$2,0,3*(A6-1)))