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IAT IISER2024MathematicsSequences and Series

Let a₁, a₂, a₃, be a sequence of real numbers. Let s_n=a₁+a₂+ +a_n . If 2 s_n=n (c+a_n ) for some real number c and for all n=1,2,3, , then which one of the following statements is Correct?

Options

  1. Aa₁, a₂, a₃, is an Arithmetic Progression.
  2. Ba₁, 2 a₂, 3 a₃, is an Arithmetic Progression.
  3. Ca₁, 2 a₂, 3 a₃, is a Geometric Progression.
  4. Da₁, a₂, a₃, is a Geometric Progression.

Correct answer

A. a₁, a₂, a₃, is an Arithmetic Progression.

Step-by-step solution

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