Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-3>Q 12

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If there are $n$ AM's between $1 & 31$ such that $7 t h$ mean : $(n - 1)$ th mean $= 5 : 9$ , then value of $n$ 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-3>Q 13

If the sum of the series,

7 + 77 + 777 + \dots \dots

to

n

terms is

S = (a / b) (10^{n + 1} - 9 n - 10)

, then

a + b

(where

a & b

are coprime numbers) is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-3>Q 14

Let one AM '

a

' & two GM's

p & q

be inserted between any two given numbers, if

p^{3} + q^{3} = k a p q

, then

k

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-3>Q 17

Given $a, b, c$ three numbers and the sum of numbers is $25$ . The numbers $2, a, b$ are in A.P. and the numbers $b, c, 18$ are consecutive terms of a G.P., then the value of $(a + \frac{c}{b})$ is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-3>Q 18

Find the sum of the first

8

terms of the series:

1 + 2 (1 + \frac{1}{n}) + 3 {(1 + \frac{1}{n})}^{2} + 4 {(1 + \frac{1}{n})}^{3} + \dots \dots . . .

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-3>Q 19

The harmonic mean of two numbers is

4

. The arithmetic mean

A

and the geometric mean

G

satisfy the relation

2 A + G^{2} = 27

. The sum of squares of those two numbers is

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-3>Q 20

Let

a, b, c

are sides of a scalene triangle, if

(a + b + c)^{3} > k (a + b - c) (b + c - a) (c + a - b)

, then the value of

k

. is

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-3>Q 22

Let the value of

x + y + z

is

15

, if

a, x, y, z, b

are in A.P. while the value of

; (1 / x) + (1 / y) + (1 / z)

is

5 / 3

if

a, x, y, z, b

are in H.P, then value of

(a^{2} + b^{2})

is

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Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-3>Q 23

If in a G.P., the ratio of the sum of the first eleven terms to the sum of the last eleven terms is

\frac{1}{8}

and the ratio of the sum of all the terms without the first nine to the sum of all the terms without the last nine is

2

, then the number of terms in the G.P is: