Let a1, a2, . . . , an and b1, b2, . . . , bn be two arithmetic progressions. Prove that the points
(a1, b1),(a2, b2), . . . ,(an, bn) are collinear.
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The first concept ,I have used, is completely dependent on graph(This concept is not available in most books directly or in other sites, but it doesn't mean that it is incorrect. Actually this is one of the laws of mathematics)(I have just presented the observation in the form of one concept)
You can also show it by using graph, by taking suitable values for a,b and d respectively,plot them in the graph and observe that they all lie on the same line(they are collinear)
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