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Show that there exists three numbers a, b, c in arithmatic progression

Source: MTRP 2017 Class 11-Short Answer Type Question: Problem 5 :-

May 26, 2020
functionarithmetic sequencealgebrabijective function

Problem Statement

Let N\mathbb{N} be the set of all natural numbers. Let f:Nā†’Nf:\mathbb{N} \to \mathbb{N} be a bijective function. Show that there exists three numbers aa, bb, cc in arithmatic progression such that f(a)<f(b)<f(c)f(a)<f(b)<f(c)
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