Question:
If $a, b, c$ are in G.P., then
If $a, b, c$ are in G.P., then
Updated On: Dec 19, 2025
- $a^2, b^2, c^2$ are in G.P.
- $a^2 (b + c),c^2 (a + b),b^2 (a + c)$ are in G.P.
- $\frac{a}{b+c} , \frac{b}{c+a}, \frac{c}{a+b} $ are in G.P.
- None of these
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
$\because a, b, c$ are in G.P.
$\therefore \frac{b}{a} = \frac{c}{b} =r$
$ \Rightarrow \frac{b^{2}}{a^{2}} = \frac{c^{2}}{b^{2}} =r^{2}$
$ \Rightarrow \frac{b^{2}}{a^{2}} = \frac{c^{2}}{b^{2}} =r^{2} $
$\Rightarrow a^{2} , b^{2} , c^{2} $ are in G.P.
$\therefore \frac{b}{a} = \frac{c}{b} =r$
$ \Rightarrow \frac{b^{2}}{a^{2}} = \frac{c^{2}}{b^{2}} =r^{2}$
$ \Rightarrow \frac{b^{2}}{a^{2}} = \frac{c^{2}}{b^{2}} =r^{2} $
$\Rightarrow a^{2} , b^{2} , c^{2} $ are in G.P.
Was this answer helpful?
0
0
Top Questions on Geometric Progression
- Let $a_n$ be the $n^{\text{th}}$ term of a decreasing infinite geometric progression. If $a_1 + a_2 + a_3 = 52$ and $a_1a_2 + a_2a_3 + a_3a_1 = 624$, then the sum of this geometric progression is:
- CAT - 2025
- Quantitative Aptitude
- Geometric Progression
- If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is 15309, then the sum of its first nine terms is:
- JEE Main - 2025
- Mathematics
- Geometric Progression
- Find the sum of the infinite geometric series: $$ S = 8 + 4 + 2 + \cdots $$ if it converges.
- BITSAT - 2025
- Mathematics
- Geometric Progression
- If \( a, b, c \) elements are in geometric progression, then \( \log a, \log b, \log c \) will be in:
- TG EDCET - 2025
- Mathematics
- Geometric Progression
- If $ a, a r, a r^2 $ are in a geometric progression (G.P.), then find the value of: $ \left| a \quad a r \right| \quad \left| a r^2 \quad a r^3 \right| = \left| a r^3 \quad a r^6 \right| $
- KEAM - 2025
- Mathematics
- Geometric Progression
View More Questions
Questions Asked in BITSAT exam
- What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
- BITSAT - 2025
- Vector Algebra
- A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W, what is the rate at which internal energy of the system increases?
- BITSAT - 2025
- Thermodynamics
- If the roots of the quadratic equation $ x^2 + 4x + k = 0 $ are real and equal, then the value of $ k $ is:
- BITSAT - 2025
- Quadratic Equations
- A simple pendulum has a time period of 2 s on Earth's surface. What is its time period at a height equal to the Earth's radius (R)? (Acceleration due to gravity at height h is \( g_h = \frac{g}{(1 + h/R)^2} \)).
- BITSAT - 2025
- Mechanics
For the reaction \( A + B \to C \), the rate law is found to be \( \text{rate} = k[A]^2[B] \). If the concentration of \( A \) is doubled and \( B \) is halved, by what factor does the rate change?
- BITSAT - 2025
- Chemical Kinetics
View More Questions
Concepts Used:
Geometric Progression
What is Geometric Sequence?
A geometric progression is the sequence, in which each term is varied by another by a common ratio. The next term of the sequence is produced when we multiply a constant to the previous term. It is represented by: a, ar1, ar2, ar3, ar4, and so on.
Properties of Geometric Progression (GP)
Important properties of GP are as follows:
- Three non-zero terms a, b, c are in GP if b2 = ac
- In a GP,
Three consecutive terms are as a/r, a, ar
Four consecutive terms are as a/r3, a/r, ar, ar3 - In a finite GP, the product of the terms equidistant from the beginning and the end term is the same that means, t1.tn = t2.tn-1 = t3.tn-2 = …..
- If each term of a GP is multiplied or divided by a non-zero constant, then the resulting sequence is also a GP with a common ratio
- The product and quotient of two GP’s is again a GP
- If each term of a GP is raised to power by the same non-zero quantity, the resultant sequence is also a GP.
If a1, a2, a3,… is a GP of positive terms then log a1, log a2, log a3,… is an AP (arithmetic progression) and vice versa