Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 14

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Let $a_{1}, a_{2}, a_{3} \dots \dots$ and $b_{1}, b_{2}, b_{3}, \dots \dots$ be arithmetic progression such that $a_{1} = 25, b_{1} = 75$ and $a_{100} + b_{100} = 100$ , then

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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-2>Q 15

If the AM of two positive numbers be three times their geometric mean then the ratio of the numbers is

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 16

If the first and

{(2 n - 1)}^{th}

terms of an A.P., a G.P. and a H.P. are equal and their

n^{th}

terms are

a, b

and

c

respectively, then

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 17

Let

a,

x, b

be in A.P.,

a, y, b

be in G.P. and

a, z, b

be in H.P. If

x = y + 2

and

a = 5 z,

then

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 18

The

p^{t h}

term

T_{p}

of

H . P .

is

q (q + p)

and

q^{t h}

term

T_{q}

is

p (p + q)

when

p > 1, q > 1

, then

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 19

a, b, c

are three distinct real numbers, which are in

G . P .

and

a + b + c = x b

, then -

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 21

If

10

harmonic means

H_{1}, H_{2}, H_{3} \dots \dots . H_{10}

are inserted between

7

and

- \frac{1}{3}

, then -

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 23

Indicate the correct alternative(s), for

0 < ϕ < \frac{π}{2}

, if

x = \sum_{n = 0}^{\infty} \cos^{2 n} ϕ, y = \sum_{n = 0}^{\infty} \sin^{2 n} ϕ

and

z = \sum_{n = 0}^{\infty} \cos^{2 n} ϕ \sin^{2 n} ϕ

. then

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 24

If

x_{1}, x_{2}, x_{3}

as well as

y_{1}, y_{2}, y_{3}

are in

G . P .

with the same common ratio, then the points

(x_{1}, y_{1}), (x_{2}, y_{2})

and

(x_{3}, y_{3})