If a, b, care in G.P., then log a", log b", log c" are in

Important Questions on Arithmetic and Geometric Progression

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

In the sequence $25,5,1,\dots ,\frac{1}{3125}$ which term is $\frac{1}{3125}$?

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

If $a, b, c$ are in G.P., then $\frac{a-b}{b-c}$ is equal to:

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

Given $\mathrm{A}=2^{65}$ and $\mathrm{B}=\left(2^{64}+2^{63}+2^{62}+\dots +2°\right)$, which of the following is true?

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

Let $a_1,a_2,{\dots ..a}_{10}$ be a G.P. If $\frac{a_3}{a_1}=25,$ then $\frac{a_9}{a_5}$ equals:
 

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

Let $a, b \& c$ be in A.P. with a common difference $d$. Then $e^{\frac{1}{c}}, e^{\frac{b}{ac}}, e^{\frac{1}{a}}$ are in

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

The product of three consecutive terms of a $G.P.$ is $512$. If $4$ is added to each of the first and the second of these terms, the three terms now form an $A.P.$, then the sum of the original three terms of the given $G.P.$ is :

HARD

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

If $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\cdots$ upto $\infty =\frac{{\mathrm{\pi }}^2}{6}$, then value of $\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+\cdots$ upto $\infty$ is

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

Let $\left|a\right|<1, \left|b\right|<1, \left|c\right|<1$ and $x=\sum _{n=0}^{\infty }{a}^n, y=\sum _{n=0}^{\infty }{b}^n, z=\sum _{n=0}^{\infty }{c}^n$. If $\frac{1}{x}, \frac{1}{y} \text{and} \frac{1}{z}$ are in Arithmetic Progression, then

MEDIUM

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

In an ordered set of four numbers, the first $3$ are in $\mathrm{AP}$ and the last $3$ are in $\mathrm{GP}$ whose common ratio is $\frac{7}{4}$. If the product of the first and fourth of these number is $49$, then the product of the second and third of these, is

MEDIUM

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

If $0<x<1,$ then $\frac{3}{2}{x}^2+\frac{5}{3}{x}^3+\frac{7}{4}{x}^4+\dots ,$ is equal to

MEDIUM

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

Let $a, b$ and $c$ be the $7^{th}, {11}^{th}$ and ${13}^{th}$ terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then $\frac{a}{c}$ is equal to:

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

The third term of a $\mathrm{G}.\mathrm{P}.$ is $9$. The product of its first five terms is 

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

If the sum of an infinite GP be $9$ and sum of first two terms be $5$ then their common ratio is …..

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

Three numbers is $\mathrm{G}.\mathrm{P}.$ with their sum is $130$ and their product is $27,000$ are _________

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

The product $2^{\frac{1}{4}}·4^{\frac{1}{16}}·8^{\frac{1}{48}}·{16}^{\frac{1}{128}}·....$ to $\infty$ is equal to:

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

The sum value of the infinite series $1+\frac{1}{5}+\frac{1}{25}+\frac{1}{125}+\frac{1}{625}+\cdots \infty$ is

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

How many digits will be there after the decimal point ${12}^{\mathrm{th}}$ term of the sequence: $32, 16, 8, 4, \dots \dots ?$

MEDIUM

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

If for $x,y\in R, x>0,$ $y={\log }_{10}x+{\log }_{10}{x}^{1/3}+{\log }_{10}{x}^{1/9}+\dots$upto $\infty$ terms and $\frac{2+4+6+\dots +2y}{3+6+9+\dots +3y}=\frac{4}{{\log }_{10}x},$ then the ordered pair $\left(x, y\right)$ is equal to

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

If $a^{\frac{1}{x}}=b^{\frac{1}{y}}=c^{\frac{1}{z}}$ and $a, b, c$ are in $\mathrm{G}.\mathrm{P}.$, then $x, y, z$  will be in

MEDIUM

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Geometric Progression

Let $a_1,a_2,a_3,\dots$, be a $\mathrm{G}.\mathrm{P}.$ such that $a_1<0,a_1+a_2=4$ and $a_3+a_4=16$. If $\sum _{i=1}^9{a}_i=4\lambda$, then $\lambda$ is equal to