Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 30

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JEE Main

IMPORTANT

Earn 100

The sum of first four terms of a geometric progression $(G . P .)$ is $\frac{65}{12}$ and the sum of their respective reciprocals is $\frac{65}{18} .$ If the product of first three terms of the $G . P .$ is $1,$ and the third term is $α,$ then $2 α$ is _________.

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Important Questions on Sequences and Series

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 31

Three positive numbers form an increasing

G . P .

If the middle term in the

G . P .

is doubled the three numbers are in an

A . P .

Then the common ratio of the

G . P .

is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 32

Three numbers whose sum is

15

are in

A . P .

If they are added by

1, 4

and

19

, respectively, they are in

G . P .

The numbers are

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 33

If

a, b, c

are positive integers forming an increasing

G . P .

,

b - a

is a perfect cube and

\log_{6} a + \log_{6} b + \log_{6} c = 6

, then

a + b + c

is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 34

The sum of series,

6 + 66 + 666 + . . . . . . . .

upto

n

term is -

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 35

The value of

x

in

(- π, π)

which satisfies the equation

8^{1 + |\cos x| + | \cos^{2} x | + | \cos^{3} x ∣ + \dots \dots \infty} = 4^{3}

is -

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 36

Three numbers whose product is

512

are in

G . P .

If

8

is added to the first and

6

to the second, the number will be in

A . P .

The numbers are -

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 37

If

a, b, c

form a

G . P .

with common ratio

r

such that

0 < r < 1

, and if

a, \frac{3 b}{2}, - 4 c

form an

A . P .

, then

r

is equal to -

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 38

The sum of the series

3 - 1 + \frac{1}{3} - \frac{1}{9} + \dots

is equal to