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

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Let $a_{1}, a_{2}, a_{3}, \dots$ . be a G.P. of increasing positive numbers. Let the sum of its $6^{th}$ and $8^{th}$ terms be $2$ and the product of its $3^{rd}$ and $5^{th}$ terms be $\frac{1}{9}$ . Then $6 (a_{2} + a_{4}) (a_{4} + a_{6})$ is equal to

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Important Questions on Sequences and Series

HARD

Mathematics>Algebra>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

The third term of a

G . P .

9

. The product of its first five terms is

EASY

Mathematics>Algebra>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

If the fifth term of a G.P. is

2 .

Then the product of its first

9

terms is

MEDIUM

Mathematics>Algebra>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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>Sequences and Series>Geometric Progressions

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 a1,a2,a3,…. be a G.P. of increasing positive numbers. Let the sum of its 6th and 8th terms be 2 and the product of its 3rd and 5th terms be 19. Then 6a2+a4a4+a6 is equal to

Important Questions on Sequences and Series

Learn and Prepare for any exam you want !

Let $a_{1}, a_{2}, a_{3}, \dots$ . be a G.P. of increasing positive numbers. Let the sum of its $6^{th}$ and $8^{th}$ terms be $2$ and the product of its $3^{rd}$ and $5^{th}$ terms be $\frac{1}{9}$ . Then $6 (a_{2} + a_{4}) (a_{4} + a_{6})$ is equal to