Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 21

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IMPORTANT

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Let $a < b < c$ be three integers such that $a, b, c$ is an arithmetic progression and $a, c, b$ is a geometric progression. What is the smallest possible value of $10 c ?$

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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 22

If in a G.P., the ratio of the sum of the first eleven terms to the sum of the last eleven terms is

\frac{1}{8}

and the ratio of the sum of all the terms without the first nine to the sum of all the terms without the last nine is

2

, then the number of terms in the G.P is:

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 23

The series

\frac{2 x}{x + 3} + {(\frac{2 x}{x + 3})}^{2} + {(\frac{2 x}{x + 3})}^{3} + \dots \dots \infty

will have a definite sum when -

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 24

If

S_{p}

denotes the sum of the series

1 + r^{p} + r^{2 p} + \dots \dots

to

\infty

and

s_{p}

denotes the sum of the series

1 - r^{p} + r^{2 p} - r^{3 p} + \dots \dots

to

\infty, | r | < 1,

then

S_{p} + s_{p}

is

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

If

\sin α, \sin β, \sin γ

are in

A . P .

and

\cos α, \cos β, \cos γ

are in

G . P .,

then

\frac{\cos^{2} α + \cos^{2} γ - 4 \cos α \cos γ}{1 - \sin α \sin γ} =

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 26

In a sequence of

21

terms first

11

terms are in A.P. with common difference

2

and last

11

terms are in G.P. with common ratio

2 .

If middle term of A.P. is equal to middle term of G.P. then, middle term in the complete sequence is

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 27

A square is drawn by joining mid-points of the sides of a square. Another square is drawn inside the second square in the same way and the process is continued indefinitely. If the side of the first square is

16 cm

, then what is the sum of the areas of all the squares?

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

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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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