If the nth term of a progression be a linear expression in n then prove that this progression is an AP.

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Solution

Let the progression be $t_{n}$
According to the question: $t_{n} = a n + b$
Let us take the consecutive difference: $t_{n} - t_{n - 1} = a n + b - a (n - 1) - b = 2 a$
As the consecutive difference is constant, the sequence is an AP by definition of an AP.

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