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Algebra Level pending

If \(a_1, a_2,a_3,\ldots\) follows a harmonic progression, and \(\displaystyle f(k) = \sum_{r=1}^n (a_r - a_k) \), then \( \dfrac {a_1} {f(1)},\dfrac {a_2} {f(2)},\dfrac {a_3} {f(3)},\ldots, \dfrac {a_n} {f(n)} \) follows a/an \(\text{__________} \).

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