Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 16

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If $n$ A.M.'s are inserted between $2$ and $38$ such that the sum of the resulting series obtained is $200$ , then the value of $n$ 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 17

If

S_{n}

denotes the sum to

n

terms of an A.P. whose first term is

a

and common difference is

d

, then

S_{n + 3} - 3 S_{n + 2} + 3 S_{n + 1} - S_{n}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 19

If

S_{n}

denotes the sum of first

n

terms of an

A . P .

and

S_{2 n} = 3 S_{n}

then

\frac{S_{3 n}}{S_{n}}

is equal to -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 20

Let $S_{n}$ denote the sum of $n$ terms of an

A . P .

whose first term is $a$ . If the common difference $d$ is given by

d = S_{n} - k S_{n - 1} + S_{n - 2}

, then

k

is equal to -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 21

If the first, second and last term of an

A . P .

are

a, b and

2 a

respectively, then its sum is

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 22

If

A_{1}, A_{2}

are two A.M.'s between two positive numbers

a

and

b

, then

(2 A_{1} - A_{2}) (2 A_{2} - A_{1})

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 23

The maximum sum of the series

100 + 98 + 96 + \dots

is

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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 29

If

(2 p)^{t h}

term of a G.P. is

q^{2}

and

(2 q)^{t h}

term is

p^{2}

, then

(p + q)^{t h}

term is