NDA 2016 Maths · Mathematics · Sequences and Series · medium

If a, b, c are in AP, then 1/bc,1/ca,1/ab are in AP. 2. If a, b, c are positive and in GP, then log a, log b, log c are in AP.

Single correct option

Consider the following statements:
1. If

a

b

c

are in AP, then

\dfrac1{bc},\dfrac1{ca},\dfrac1{ab}

are in AP.
2. If

a

b

c

are positive and in GP, then

\log a

\log b

\log c

are in AP.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (C) Both 1 and 2

Statement 1:

\dfrac1{bc}=\dfrac{a}{abc}

\dfrac1{ca}=\dfrac b{abc}

\dfrac1{ab}=\dfrac c{abc}

; these are in AP because

a,b,c

are. Statement 2:

b^2=ac

gives

2\log b=\log a+\log c

, so the logarithms are in AP. Both statements are correct.

Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake