Question

Assertion :Let three distinct positive real numbers $a,b,c$ are in G.P., then $a^2,b^2,c^2$ are in G.P. Reason: If we square each term of a G.P., then the resulting sequence is also in G.P.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

If we square each term of a G.P., then the resulting sequence is also in G.P.

Proof:

$a,b,c$ are in G.P.

$\frac{b}{a}=\frac{c}{b}$ .........(1)

For, $a^2,b^2,c^2$

$\frac{b^2}{a^2}=\frac{b}{a}\times \frac{b}{a}$

$=\frac{c}{b}\times \frac{c}{b}$ (from eq. (1))

$=\frac{c^2}{b^2}$

Thus $a^2,b^2,c^2$ will also be in GP.