Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 28

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The sum of an infinite G.P. is $x$ and the common ratio $r$ is such that $| r | < 1$ . If the first term of the G.P. is $2$ , then which one of the following is correct?

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Important Questions on Sequences and Series

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 29

Let

(n > 1)

be a positive integer, then the largest integer

m

such that

(n^{m} + 1)

divides

(1 + n + n^{2} + \dots \dots + n^{127})

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 30

If

A = 1 + r^{z} + r^{2 z} + r^{3 z} + \dots \infty

, then the value of

r

will be

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 31

In a certain test there are

n

questions. In the test

2^{n - i}

students gave wrong answers to atleast

i

questions, where

i = 1, 2, \dots ., n .

If the total number of wrong answers given is

2047,

then

n

is equal to

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 32

Let

a, b, c, d

and

e

be distinct positive numbers. If

a, b, c

and

\frac{1}{c}

,

\frac{1}{d}

,

\frac{1}{e}

both are in

AP

and

b, c, d

are in

GP

, then

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 33

If

b - c, b x - c y, b x^{2} - c y^{2} (b, c \neq 0)

are in

G . P .

, then the value of

(\frac{b x + c y}{b + c}) (\frac{b x - c y}{b - c})

is

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 34

If

a, b, c

are real numbers forming an

A . P .

and

3 + a, 2 + b, 3 + c

, are in

G . P .,

then minimum value of

a c

is

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 35

The second and fourth terms of a geometric sequence are

2

and

6 .

Which of the following is a possible first term?

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 36

The value of the infinite product

6^{\frac{1}{2}} \times 6^{\frac{1}{2}} \times 6^{\frac{3}{8}} \times 6^{\frac{1}{4}} \times \dots

is