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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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Important Questions on Progression and Series

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Archives>Q 1

Let

S_{k}, k = 1, 2 . . . ., 100,

denote the sum of the infinite geometric series whose first term is

\frac{k - 1}{k!}

and the common ratio is

\frac{1}{k},

then the value of

\frac{100^{2}}{100!} + \sum_{k = 1}^{100} |(k^{2} - 3 k + 1) S_{k}|

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Archives>Q 2

Let

a_{1}, a_{2}, a_{3}, . . . ., a_{11}

be real numbers satisfying

a_{1} = 15, 27 - 2 a_{2} > 0

and

a_{k} = 2 a_{k - 1} - a_{k - 2}

for

k = 3, 4, . . ., 11

. If

\frac{a_{1}^{2} + a_{2}^{2} + . . . . + a_{11}^{2}}{11} = 90,

then the value of

\frac{a_{1} + a_{2} + . . . + a_{11}}{11}

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Archives>Q 3

Let

a_{1}, a_{2}, a_{3}, . . . a_{100}

be an arithmetic progression with

a_{1} = 3

and

S_{p} = \sum_{i = 1}^{p} a_{i}, 1 \leq p \leq 100 .

For any interger

n

with

1 \leq n \leq 20,

let

m = 5 n .

\frac{S_{m}}{S_{n}}

does not depend on

n,

then

a_{2}

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Archives>Q 4

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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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Archives>Q 5

Let

a, b, c

be positive integers such that

\frac{b}{a}

is an integer. If

a, b, c

are in geometric progression and the arithmetic mean of

a, b, c

b + 2,

then value of

\frac{a^{2} + a - 14}{a + 1}

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Archives>Q 6

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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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Archives>Q 7

The sides of a right angled triangle are in arithematic progression

(A . P)

. If the triangle has area

24

, Then what is the length of its smallest side?

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Archives>Q 8

Let

X

be the set consisting of the first

2018

terms of the arithmetic progression

1, 6, 11, . . .,

and

Y

be the set consisting of the first

2018

terms of the arithmetic progression

9, 16, 23, . . . .,

Then , the number of elements in the set

X \cup Y

Let Sn=∑k=14n-1kk+12 k2. Then Sn can take value s

Important Questions on Progression and Series

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Let $S_{n} = \sum_{k = 1}^{4 n} {(- 1)}^{\frac{k (k + 1)}{2} k^{2} .}$ Then $S_{n}$ can take value $(s)$