Let A1, A2, A3, … be an increasing geometric progression of positive real numbers. If A1A3A5A7 = \(\frac {1}{1296}\) and A2 + A4 = \(\frac {7}{36}\) then, the value of A6 + A8 + A10 is equal to
- 33
- 37
- 43
- 47
The Correct Option is C
Solution and Explanation
\(\frac {A_4}{r^3}. \frac {A_4}{r} . A_4r . A_4r^3 = \frac {1}{1296}\)
\(A_4 = \frac 16\)
\(A_2 = \frac {7}{36} - \frac 16\)
\(A_2= \frac {1}{36}\)
So, \(A_6 + A_8 + A_{10} = 1 + 6 + 36\)
\(= 43\)
So, the correct option is (C): \(43\)
Top Questions on Geometric Progression
- If \( a_1, a_2, a_3, \ldots \) are in increasing geometric progression such that \[ a_1 + a_3 + a_5 = 21, a_1 a_3 a_5 = 64, \] then \( a_1 + a_2 + a_3 \) is:
- JEE Main - 2026
- Mathematics
- Geometric Progression
- In a Geometric Progression (G.P.), if the third term is 4, then the product of the first 5 terms is
- IPU CET - 2025
- Mathematics
- 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
- 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
Questions Asked in JEE Main exam
The equivalent resistance between the points \(A\) and \(B\) in the given circuit is \[ \frac{x}{5}\,\Omega. \] Find the value of \(x\).
- JEE Main - 2026
- Current electricity
Method used for separation of mixture of products (B and C) obtained in the following reaction is:
- JEE Main - 2026
- p -Block Elements
- Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media A and B are \(2.4 \times 10^8\) m/s and \(2.7 \times 10^8\) m/s, respectively, then the value of critical angle is :
- JEE Main - 2026
- Newtons Laws of Motion
In the following \(p\text{–}V\) diagram, the equation of state along the curved path is given by \[ (V-2)^2 = 4ap, \] where \(a\) is a constant. The total work done in the closed path is:
- JEE Main - 2026
- Thermodynamics
Let \( ABC \) be a triangle. Consider four points \( p_1, p_2, p_3, p_4 \) on the side \( AB \), five points \( p_5, p_6, p_7, p_8, p_9 \) on the side \( BC \), and four points \( p_{10}, p_{11}, p_{12}, p_{13} \) on the side \( AC \). None of these points is a vertex of the triangle \( ABC \). Then the total number of pentagons that can be formed by taking all the vertices from the points \( p_1, p_2, \ldots, p_{13} \) is ___________.
- JEE Main - 2026
- Coordinate Geometry
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