Select Goal &
City
Select Goal
Explore
Question:
The third term of a G.P. is 9. The product of its first five terms is
The third term of a G.P. is 9. The product of its first five terms is
Updated On: Jul 2, 2024
- $3^{10}$
- $3^5$
- $3^{12}$
- $3^9$
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
$Let \frac{a}{r^{2}}.\frac{a}{r}.a.ar.ar^{2} $ are in G.P., Given a = 9
$\therefore\, product =9^{5}=3^{10}$
Was this answer helpful?
1
1
Top Questions on Geometric Progression
- In an increasing geometric progression of positive terms, the sum of the second and sixth terms is \[ \frac{70}{3} \] and the product of the third and fifth terms is 49. Then the sum of the \(4^\text{th}, 6^\text{th}\), and \(8^\text{th}\) terms is:
- JEE Main - 2024
- Mathematics
- Geometric Progression
- If the range of $f(\theta) = \frac{\sin^4\theta + 3\cos^2\theta}{\sin^4\theta + \cos^2\theta}, \, \theta \in \mathbb{R}$ is $[\alpha, \beta]$, then the sum of the infinite G.P., whose first term is $64$ and the common ratio is $\frac{\alpha}{\beta}$, is equal to ____.
- JEE Main - 2024
- Mathematics
- Geometric Progression
- If in a G.P. of64terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P., then the common ratio of the G.P. is equal to:
- JEE Main - 2024
- Mathematics
- Geometric Progression
- Let \( a, ar, ar^2, \dots \) be an infinite G.P. If \[ \sum_{n=0}^\infty ar^n = 57 \quad \text{and} \quad \sum_{n=0}^\infty a^3 r^{3n} = 9747, \] then \( a + 18r \) is equal to:
- JEE Main - 2024
- Mathematics
- Geometric Progression
- Let \(α\) and \(β\) the roots of equation \(px^2 + qx - r = 0\), where \(P≠ 0\). If \(p,q,r\) be the consecutive term of non constant G.P and \(\frac{1}{α} + \frac{1}{β} = \frac{3}{4}\) then the value of \((α - β)^2\) is:
- JEE Main - 2024
- Mathematics
- Geometric Progression
View More Questions
Questions Asked in KCET exam
- The energy gap of an LED is 2.4 eV. When the LED is switched ‘ON’, the momentum of the emitted photons is
- KCET - 2023
- Semiconductor electronics: materials, devices and simple circuits
- In which one of the following pairs, both the elements does not have (n-1)d10ns2 configuration in its elementary state?
- KCET - 2023
- subshell electronic configuration
- An equiconvex lens made of glass of refractive index \(\frac{3}{2}\) has focal length f in air. It is completely immersed in water of refractive index \(\frac{4}{3}\). The percentage change in the focal length is
- KCET - 2023
- Ray optics and optical instruments
- A metallic rod of length 1 m held along east-west direction is allowed to fall down freely. Given horizontal component of earth’s magnetic field BH = 3 × 10-5 T. The emf induced in the rod at an instant t = 2s after it is released is ( Take g = 10 ms-2 )
- KCET - 2023
- Faradays laws of induction
- The modulus of the complex number \(\frac{(1+i)^2(1+3i)}{(2-6i)(2-2i)}\) is
- KCET - 2023
- complex numbers
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
SUBSCRIBE TO OUR NEWS LETTER
COLLEGE NOTIFICATIONSEXAM NOTIFICATIONSNEWS UPDATES
Download the Collegedunia app on 
© 2024 Collegedunia Web Pvt. Ltd. All Rights Reserved