The common sum is 18.
What is a common sum?
The following item in an arithmetic sequence is obtained by adding or subtracting a specified amount (the common sum). To find the common sum in an arithmetic sequence, add the first term from the second term.
Here,
We have a number on a vertex.
It will be counted in 3 different faces since any vertex is the intersection of three edges.
Therefore, each number 1, 2, .... 7,8 will be added to the total sum 3 times.
Our total sum is 3(1+2+....+8) = 108.
since there are 6 faces in a cube, we get
our common sum is :
= 108/6
= 18
Hence, the common sum is 18.
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