Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.2>Q 7

EASY

JEE Advanced

IMPORTANT

Earn 100

If the sum of the first $10$ terms of a certain $GP$ is equal to $244$ times the sum of first $5$ terms, then the common ratio is

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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 8

If

a, 2 b, 3 c

are in

AP

and

a, b, c

(distinct) are in

GP

, then the common ratio is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.2>Q 9

If a

GP

having an even number of terms and the sum of all terms is five times the sum of terms occupying odd places, then the common ratio will be

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.2>Q 10

For

n \geq 3

,

n^{th}

roots of unity form

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.2>Q 11

If

1 + a + a^{2} + a^{3} + \dots + a^{n} = (1 + a) (1 + a^{2}) (1 + a^{4})

then

n

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.2>Q 12

The rational number

2.357357357 \dots

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 3 - Sequence and Series>Work Book Exercise 3.2>Q 13

9^{\frac{1}{3}} \cdot 9^{\frac{1}{9}} \cdot 9^{\frac{1}{27}} \dots

is equal to

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 14

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

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