If a b c are in GP where a gt 0 b gt 0 c gt 0 then which of the following are correct 1 a2...........

Mathematics (NDA) Number System

If a, b, c are in GP where a > 0, b > 0, c > 0, then which of the following are correct ?

1. a², b², c² are in GP

2. 1/a, 1/b' 1/care m GP

3. √a, √b , √c are in GP

Select the correct answer using the code given below :

This questions was previously asked in

2022 NDA -1 Math

1 and 2 only

2 and 3 only

1 and 3 only

1, 2 and 3

- If \( a, b, c \) are in GP, then \( b = ar \) and \( c = ar^2 \) for some common ratio \( r \).

- Statement 1: \( a^2, b^2, c^2 \) can be shown as \( (ar)^2, (ar^2)^2 \), and it follows the pattern of a GP with the same common ratio.

- Statement 2: \( \frac{1}{a}, \frac{1}{b}, \frac{1}{c} \) will also be in GP since inverses of terms in GP still form a GP.

- Statement 3: \( \sqrt{a}, \sqrt{b}, \sqrt{c} \) are in GP because roots of GP terms follow a pattern similar to the original sequence.

The correct answer is Option 4: 1, 2, and 3.

Submit Error