Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 21

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If $p, q, r$ in harmonic progression and $p & r$ be different having same sign then the roots of the equation $p x^{2} + q x + r = 0$ are

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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 22

If

x > 1, y > 1, z > 1

are in GP, then

\frac{1}{1 + \ln x}, \frac{1}{1 + \ln y}

,

\frac{1}{1 + \ln z}

are in

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 23

If

ln (a + c), ln (c - a), ln (a - 2 b + c)

are in A.P., then

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

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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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