Let a < 1 , b < 1 , c < 1 and x = ∑ n = 0 ∞ a n , y = ∑ n = 0 ∞ b n , z = ∑ n = 0 ∞ c n . If 1 x , 1 y and 1 z are in Arithmetic Progression, then

a , b and c are in Arithmetic Progression.

a , 2 b and c are in Arithmetic Progression.

a , b and c satisfy 2 b 2 = a c .

a , b and c are in Geometric Progression.

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

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The value of ${(0.36)}^{\log_{0.25} (\frac{1}{3} + \frac{1}{3^{2}} + \frac{1}{3^{3}} + . . . . . u p t o \infty)}$ is

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Important Questions on Sequences and Series

MEDIUM

Mathematics>Algebra>Sequences and Series>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:

EASY

Mathematics>Algebra>Sequences and Series>Geometric Progression

Let

|a| < 1, |b| < 1, |c| < 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} and \frac{1}{z}

are in Arithmetic Progression, then

EASY

Mathematics>Algebra>Sequences and Series>Geometric Progression

The sum value of the infinite series

1 + \frac{1}{5} + \frac{1}{25} + \frac{1}{125} + \frac{1}{625} + \dots \infty

EASY

Mathematics>Algebra>Sequences and Series>Geometric Progression

The common ratio of

G . P .

a^{m - n}, a^{m}, a^{m + n}

EASY

Mathematics>Algebra>Sequences and Series>Geometric Progression

The product

2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}} \cdot . . . .

\infty

is equal to:

EASY

Mathematics>Algebra>Sequences and Series>Geometric Progression

What is the sum value of the geometric series

6 + 3 + 3 / 2 + 3 / 4 + \dots \infty ?

EASY

Mathematics>Algebra>Sequences and Series>Geometric Progression

How many digits will be there after the decimal point

12^{th}

term of the sequence:

32, 16, 8, 4, \dots \dots ?

EASY

Mathematics>Algebra>Sequences and Series>Geometric Progression

Given

A = 2^{65}

and

B = (2^{64} + 2^{63} + 2^{62} + \dots + 2 °)

, which of the following is true?

EASY

Mathematics>Algebra>Sequences and Series>Geometric Progression

The third term of a

G . P .

9

. The product of its first five terms is

EASY

Mathematics>Algebra>Sequences and Series>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>Sequences and Series>Geometric Progression

a, b, c

are in G.P., then

\frac{a - b}{b - c}

is equal to:

EASY

Mathematics>Algebra>Sequences and Series>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 :

EASY

Mathematics>Algebra>Sequences and Series>Geometric Progression

{(1.05)}^{50} = 11.658

, then

\sum_{n = 1}^{49} {(1.05)}^{n}

equals

EASY

Mathematics>Algebra>Sequences and Series>Geometric Progression

$A$ set $P$ is taken such that $P = \{2 / 3^{p} ∣ p$ is a natural number $} .$ What will be the sum of elements of set $P ?$

EASY

Mathematics>Algebra>Sequences and Series>Geometric Progression

n^{th}

term of a progression

a, a r, a r^{2}, \dots \dots

EASY

Mathematics>Algebra>Sequences and Series>Geometric Progression

In the sequence

25, 5, 1, \dots, \frac{1}{3125}

which term is

\frac{1}{3125}

EASY

Mathematics>Algebra>Sequences and Series>Geometric Progression

4, a, 9

are in G.P., then

a =

_____

EASY

Mathematics>Algebra>Sequences and Series>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

EASY

Mathematics>Algebra>Sequences and Series>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>Sequences and Series>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:

The value of 0.36log0.25⁡13+132+133+.....upto ∞ is

Important Questions on Sequences and Series

Learn and Prepare for any exam you want !

The value of ${(0.36)}^{\log_{0.25} (\frac{1}{3} + \frac{1}{3^{2}} + \frac{1}{3^{3}} + . . . . . u p t o \infty)}$ is