The points (n, u) of an arithmetic sequence are always collinear
The points are given as:
Points = (n, u)
The nth term of an arithmetic sequence is represented as:
Tn = a + (n - 1)d
Expand the bracket
Tn = a + nd - d
Collect the like terms
Tn = -d + a + nd
Evaluate the like terms
Tn = -d + a + nd
The above is a linear equation
All points on a the line of a linear equation are always on the same line, this means that they are collinear
Hence, the points (n, u) of an arithmetic sequence are always collinear
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