Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 41

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Four geometric means are inserted between the numbers $2^{11} - 1$ and $2^{11} + 1$ The product of these geometric means is

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Important Questions on Sequences and Series

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 42

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 -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 43

If

a, b, c

are three distinct real numbers and they are in a

G . P .

If

a + b + c = x b

, then -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 44

The product

2^{1 / 4} \cdot 4^{1 / 8} \cdot 8^{1 / 16} \dots

to

\infty

equal to -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 45

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 -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 46

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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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 47

If

x, y, z

are in

A . P .

,

a x, b y, c z

are in

G . P .

and

\frac{1}{a}, \frac{1}{b}, \frac{1}{c}

are in

A . P .

, then

\frac{x}{z} + \frac{z}{x}

is equal to -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 48

If the second, third and sixth terms of an

A . P .

are distinct and form consecutive terms of a

G . P .

, then the common ratio of the

G . P .

is -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 49

The sum of three numbers in

G P

is

56 .

If we subtract

1, 7, 21

from these numbers in that order, we obtain an

A P .

Then, three numbers are