Questions & Answers

Question

Answers

A. \[{{\text{a}}^{\text{2}}}{\text{,b}}{}^{\text{2}}{\text{,}}{{\text{c}}^{\text{2}}}\]are in G.P

B. \[{{\text{a}}^{\text{2}}}{\text{(b + c),}}{{\text{c}}^{\text{2}}}{\text{(a + b),b}}{}^{\text{2}}{\text{(a + c)}}\]are in G.P

C. \[\dfrac{{\text{a}}}{{{\text{b + c}}}}{\text{,}}\dfrac{{\text{b}}}{{{\text{a + c}}}}{\text{,}}\dfrac{{\text{c}}}{{{\text{a + b}}}}\]are in G.P

D. None of these

Answer
Verified

As given that a, b, c are in G.P

As we know that \[{{\text{b}}^{\text{2}}}{\text{ = ac}}\]

Hence on squaring both the side of the above equation we can get

\[

{{\text{(}}{{\text{b}}^{\text{2}}}{\text{)}}^{\text{2}}}{\text{ = (ac}}{{\text{)}}^{\text{2}}} \\

{{\text{(}}{{\text{b}}^{\text{2}}}{\text{)}}^{\text{2}}}{\text{ = (}}{{\text{a}}^{\text{2}}}{\text{)(}}{{\text{c}}^{\text{2}}}{\text{)}} \\

\]

Hence, \[{{\text{a}}^{\text{2}}}{\text{,b}}{}^{\text{2}}{\text{,}}{{\text{c}}^{\text{2}}}\]are in G.P

And so option(a) is our correct answer.

Sequences are lists of numbers placed in a definite order according to given rules. The series corresponding to a sequence is the sum of the numbers in that sequence. Series can be arithmetic, meaning there is a fixed difference between the numbers of the series, or geometric, meaning there is a fixed factor.