Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 24

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Consider that $10$ Arithmetic means are inserted between $3$ and $7$ and their sum is $a$ . Again consider that the sum of five numbers in Arithmetic Progression is $30$ and the value of middle terms is $b$ . Then $a + b$ equals

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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 27

Which term of the

G . P .

18, - 12, 8, \dots

is

\frac{512}{729}

?

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 28

The third term of a G.P. is

3

The product of its first five terms is

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 35

If

g_{1}, g_{2}, g_{3}

are three geometric means between two positive numbers

a

and

b

, then

g_{1} g_{3}

is equal to -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 36

If

x, y, z

are three geometric means between

6

and

54

, then

z

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 39

Let

a_{n}

be the

n th

term of a

GP

of positive numbers. If

\sum_{n = 1}^{100} a_{2 n} = α

and

\sum_{n = 1}^{100} a_{2 n - 1} = β

, such that

α \neq β

then the common ratio is

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 40

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

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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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 -