Let a , b & c be in A.P. with a common difference d . Then e 1 c , e b a c , e 1 a are in

G.P. with common ratio e d b 2 - d 2

EASY

Earn 100

Let the first term a and the common ratio $r$ of a geometric progression be positive integers. If the sum of squares of its first three terms is $33033$ , then the sum of these three terms is equal to

53.33% studentsanswered this correctly

Important Questions on Arithmetic and Geometric Progression

HARD

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

If $m$ is the $A . M .$ of two distinct real numbers $I$ and $n$ $(I, n > 1)$ and $G_{1}, G_{2} and G_{3}$ are three geometric means between $I and n$ , then $G_{1}^{4} + 2 G_{2}^{4} + G_{3}^{4}$ equals

EASY

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

The product of three consecutive terms of a

G . P .

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 :

MEDIUM

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

Let

a_{1}, a_{2}, a_{3}, \dots

, be a

G . 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 λ

, then

λ

is equal to

MEDIUM

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

Let

α

and

β

be the roots of

x^{2} - 3 x + p = 0

and

γ

and

δ

be the roots of

x^{2} - 6 x + q = 0 .

α, β, γ, δ

from a geometric progression. Then ratio

(2 q + p) : (2 q - p)

MEDIUM

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

Let

a, b

and

c

be the

7^{t h}, 11^{t h}

and

13^{t h}

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:

HARD

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

The sum of the first three terms of $G . P$ is $S$ and their products is $27$ . Then all such $S$ lie in

HARD

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

Let

a_{n}

be the

n^{t h}

term of a G.P. of positive terms. If

\sum_{n = 1}^{100} a_{2 n + 1} = 200

and

\sum_{n = 1}^{100} a_{2 n} = 100,

then

\sum_{n = 1}^{200} a_{n}

is equal to:

HARD

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

a = 1 + 2 + 4 + \dots \dots

up to

n

terms,

b = 1 + 3 + 9 + \dots \dots

up to

n

terms and

c = 1 + 5 + 25 + \dots \dots

up to

n

terms, then

Δ = |\begin{matrix} a & 2 b & 4 c \\ 2 & 2 & 2 \\ 2^{n} & 3^{n} & 5^{n} \end{matrix}| =

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:

MEDIUM

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

Let

a, b

and

c

be in

G . P .

with common ratio

r,

where

a \neq 0

and

0 < r \leq \frac{1}{2} .

3 a, 7 b

and

15 c

are the first three terms of an

A . P .,

then the

4^{t h}

term of this

A . P .

is :

HARD

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

Let

a, b, c, d and p

be non-zero distinct real numbers such that

(a^{2} + b^{2} + c^{2}) p^{2} - 2 (a b + b c + c d) p + (b^{2} + c^{2} + d^{2}) = 0

. Then

MEDIUM

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

If the

2^{n d}, 5^{t h}

and

9^{t h}

terms of a non-constant arithmetic progression are in geometric progression, then the common ratio of this geometric progression is

EASY

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

a^{\frac{1}{x}} = b^{\frac{1}{y}} = c^{\frac{1}{z}}

and

a, b, c

are in

G . P .

, then

x, y, z

will be in

EASY

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

The third term of a

G . P .

9

. The product of its first five terms is

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}{a c}}, e^{\frac{1}{a}}

are in

MEDIUM

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

If the fifth term of a G.P. is

2 .

Then the product of its first

9

terms is

MEDIUM

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

The three sides of a right angled triangle are in

G P

(geometric progression). If the two acute angles be

α

and

β,

then

\tan α

and

\tan β

are

MEDIUM

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

α, β

and

γ

are three consecutive terms of a non-constant G.P. Such that the equations

α x^{2} + 2 β x + γ = 0

and

x^{2} + x - 1 = 0

have a common root, then

α (β + γ)

is equal to:

MEDIUM

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

If three distinct numbers

a, b, c

are in G.P. and the equations

a x^{2} + 2 b x + c = 0

and

d x^{2} + 2 e x + f = 0

have a common root, then which one of the following statements is correct?

MEDIUM

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

The sum of the

3^{r d}

and the

4^{t h}

terms of a

G . P .

60

and the product of its first three terms is

1000.

If the first term of this

G . P .

is positive, then its

7^{t h}

term is:

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the sum of these three terms is equal to

Important Questions on Arithmetic and Geometric Progression

Learn and Prepare for any exam you want !

Let the first term a and the common ratio $r$ of a geometric progression be positive integers. If the sum of squares of its first three terms is $33033$ , then the sum of these three terms is equal to