Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.2>Q 14

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IMPORTANT

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If $b_{1}, b_{2}$ and $b_{3}$ $(b_{1} > 0)$ are three successive terms of a $GP$ with common ratio $r$ , then the possible value of $r$ for which the inequality $b_{3} > 4 b_{2} - 3 b_{1}$ holds, is given by

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Important Questions on Sequence and Series

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.2>Q 15

If

S

denotes the sum to infinity and

S_{n}

denotes the sum of

n

terms of the series

1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots,

such that

S - S_{n} < \frac{1}{1000},

then the least value of

n

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.3>Q 1

The first term of

H P

having

k^{t h}

term equal to

\frac{1}{a + (k - 1) d},

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.3>Q 2

If

a, b, c

and

d

are distinct positive real numbers in

HP

, then

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.3>Q 3

The

4 t h

term of the sequence

3, \frac{3}{2}, 1, . . .

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.3>Q 4

If

|x| < 1,

then

1 + 3 x + 5 x^{2} + 7 x^{3} + \dots

is equal to

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.3>Q 5

The sum of

n

terms of the series

1 + 2 (1 + \frac{1}{n}) + 3 {(1 + \frac{1}{n})}^{2} + \dots

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.3>Q 6

If

a, b, c, d

and

p

are 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}) \leq 0,

then

a, b, c

and

d

are in

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.3>Q 7

If

x, y, z

and

w

are non-zero real numbers such that

(x^{2} + y^{2} + z^{2}) (y^{2} + z^{2} + w^{2}) \leq {(x y + y z + z w)}^{2}

, then

x, y, z

and

w

are in