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Let $a_{1}, a_{2}, a_{3}, \dots .$ be in harmonic progression with $a_{1} = 5$ and $a_{20} = 25$ . The least positive integer $n$ for which $a_{n} < 0$ is

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Important Questions on Sequences and Series

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IMPORTANT

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

Let

S_{n} = \sum_{k = 1}^{4 n} (- 1)^{\frac{k (k + 1)}{2}} k^{2} .

Then

S_{n}

can take value

(s)

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-3>Q 13

A pack contains

n

cards numbered from

1

n .

Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is

1224 .

If the smaller of the numbers on the removed cards is

k,

then

k - 20 =

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-3>Q 15

Suppose that all the terms of an arithmetic progression (

A . P .

) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is

6 : 11

and the seventh term lies in between

130

and

140

, then the common difference of this

A . P .

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-3>Q 16

Let

a_{1}, a_{2}, a_{3}, \dots

be terms of an

AP

. If

\frac{a_{1} + a_{2} + \dots + a_{p}}{a_{1} + a_{2} + \dots + a_{q}} = \frac{p^{2}}{q^{2}}, p \neq q

, then

\frac{a_{6}}{a_{21}}

equals

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

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

are in

HP

, then the expression

a_{1} a_{2} + a_{2} a_{3} + \dots + a_{n - 1} a_{n}

is equal to

EASY

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

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then, the common ratio of this progression equals

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

A person is to count

4500

currency notes. Let

a_{n}

denote the number of notes he counts in the

n^{t h}

minute. If

a_{1} = a_{2} = \dots = a_{10} = 150

and

a_{10}

a_{11}, \dots

are in an

A . P .

with common difference

- 2

, then the time taken by him to count all notes is

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

A man saves

Rs . 200

in each of the first three months of his service. In each of the subsequent months, his savings increases by

Rs . 40

more than the savings of immediately previous month. His total saving from the start of service will be

Rs . 11040

after

Let a1, a2, a3,…. be in harmonic progression with a1=5 and a20=25. The least positive integer n for which an<0 is

Important Questions on Sequences and Series

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Let $a_{1}, a_{2}, a_{3}, \dots .$ be in harmonic progression with $a_{1} = 5$ and $a_{20} = 25$ . The least positive integer $n$ for which $a_{n} < 0$ is