Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 24

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IMPORTANT

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If the $(m + 1)^{t h}, (n + 1)^{t h} & (r + 1)^{t h}$ terms of an AP are in GP $& m, n, r$ are in H P, then the ratio of the common difference to the first term of the AP is -

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Important Questions on Sequences and Series

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 25

The quadratic equation whose roots are the A.M. and H.M. between the roots of the equation,

2 x^{2} - 3 x + 5 = 0

is -

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 26

If the sum of the first

n

natural numbers is

\frac{1}{5}

times the sum of the their squares, then the value of

n

is.

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 27

Suppose

p

is the first of

n (n > 1)

AM's between two positive numbers

a

and

b

, then value of

p

is

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 29

Sum of the

n

terms of the series

\frac{3}{1^{2}} + \frac{5}{1^{2} + 2^{2}} + \frac{7}{1^{2} + 2^{2} + 3^{2}} + \dots \dots

is

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 33

Let

a_{1}, a_{2}, \dots, a_{10}

be in

AP

and

h_{1}, h_{2}, \dots, h_{10}

be in

HP

. If

a_{1} = h_{1} = 2

and

a_{10} = h_{10} = 3

, then

a_{4} h_{7}

is

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 34

Equation of a straight line passing through

(1, 4)

if the sum of its positive intercepts on the coordinate axis is the smallest is -

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 35

The value of the sum

\sum_{n = 1}^{13} (i^{n} + i^{n + 1}),

where

i = \sqrt{- 1},

equals

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 1

The AM of the series

1, 2, 4, 8, 16, . . ., 2^{n}

is