Sequences and Series: Reciprocal AP MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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Reciprocal APMediumQuestion 210010

Question

If a, b, c are in AP, then 1/bc, 1/ca, 1/ab are in:

A
AP
Correct
B
GP
C
HP
D
None

Correct answer

Explanation

If a, b, c are in AP (2b = a+c), then dividing 1/(abc) from each side: (a/abc), (b/abc), (c/abc) etc. 1/bc, 1/ca, 1/ab are in AP since 2/ca = 1/bc + 1/ab → 2 = c/b + a/b → 2b = a+c ✓.

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