Type of numbers (2)

Algebra Level 3

\[ \begin{eqnarray} \large A &=& \{a_1,a_2, a_3, \ldots \} \\ \large B &=& \{ a_2 - a_1, a_3 - a_2, a_4 - a_3 , \ldots \} \end{eqnarray} \]

Above shows two sets with infinite number of elements. Each term of set \(A\) can be represented as a difference of cubes of 2 consecutive whole numbers. What set \(B\) is in what kind of progression?

Details and Assumptions:

  • G.P denotes geometric progression.
  • H.P denotes harmonic progression.
  • A.P denotes arithmetic progression.

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