GATE 2015 EE (EE2) – Question 9

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 2 marks · Multiple choice

P,R,S,T,U form an arithmetic sequence. Which also do? I: 2P,2R,2S,2T,2U. II: P−3,R−3,S−3,T−3,U−3. III: P²,R²,S²,T²,U².

I only
I and II
II and III
I and III

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Show answer and explanation

Correct answer: (B) I and II

Explanation

Let the original common difference be d. Multiplying every term by two changes the difference to 2d, so I remains arithmetic. Subtracting the same constant leaves each difference d, so II also remains arithmetic.

For squared terms, successive differences are 2ad+d² and then 2ad+3d², generally unequal. Thus III is not guaranteed arithmetic. The correct choice is **I and II, B**.

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