NDA 2024 Maths · Mathematics · Sequences and Series · medium

For two positive numbers, (GM)^2=AMtimesHM. 2. If a,b,c are in AP, then 2^a,2^b,2^c are in AP.

Single correct option

Which of the statements is/are correct?
1. For two positive numbers,

(\text{GM})^2=\text{AM}\times\text{HM}

.
2. If

a,b,c

are in AP, then

2^a,2^b,2^c

are in AP.

Show answer and solution

Answer: (A) 1 only

For positive

p,q

: AM

=\frac{p+q}{2}

, HM

=\frac{2pq}{p+q}

, product

=pq=

^2

, so 1 is true. If

b-a=c-b=d

then

2^b/2^a=2^c/2^b=2^d

, a constant ratio, so the powers are in GP, not AP; 2 is false.

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