How to extend m + n = P + Q AP + AQ = am + an to three terms in arithmetic sequence

How to extend m + n = P + Q AP + AQ = am + an to three terms in arithmetic sequence

The general term formula of arithmetic sequence an = a1 + (n-1) d
I don't quite understand you, do I
Let K + m + n = x + y + Z
ak+am+an=a1+(k-1)d+a1+(m-1)d+a1+(n-1)d=3a1+(k+m+n-3)d
ax+ay+az=a1+(x-1)d+a1+(y-1)d+a1+(z-1)d=3a1+(x+y+z-3)d
So AK + am + an = ax + ay + AZ

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