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JEE Main

IMPORTANT

Earn 100

Let the sum of the first $n$ terms of a non-constant $A . P ., a_{1}, a_{2}, a_{3}, . . . ., a_{n}$ be $50 n + \frac{n (n - 7)}{2} A,$ where $A$ is a constant. If $d$ is the common difference of this $A . P .$ , then the ordered pair $(d, a_{50})$ is equal to

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Important Questions on Sequences and Series

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th April 2019 Shift 2>Q 72

The sum of the series

1 + 2 \times 3 + 3 \times 5 + 4 \times 7 + \dots

upto

11^{t h}

term is:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th April 2019 Shift 2>Q 73

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If

99

more identical balls are added to the total number of balls used in forming the equilateral triangle, then all these balls can be arranged in a square, whose each side contains exactly

2

balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th April 2019 Shift 2>Q 74

If the sum and product of the first three terms in an

A . P .

are

33

and

1155

, respectively, then a value of its

11^{t h}

term is:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th January 2019 Shift 1>Q 75

a, b

and

c

be three distinct real numbers in G.P. and

a + b + c = x b,

then

x

cannot be:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th January 2019 Shift 1>Q 76

Let

a_{1}, a_{2}, \dots, a_{30}

be an A.P.,

S = \sum_{i = 1}^{30} a_{i}

and

T = \sum_{i = 1}^{15} a_{(2 i - 1)} .

a_{5} = 27

and

S - 2 T = 75,

then

a_{10}

is equal to:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th January 2019 Shift 2>Q 77

The sum of the following series

1 + 6 + \frac{9 (1^{2} + 2^{2} + 3^{2})}{7} + \frac{12 (1^{2} + 2^{2} + 3^{2} + 4^{2})}{9} + \frac{15 (1^{2} + 2^{2} + \dots + 5^{2})}{11} + . . . .

up to

15

terms, is:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 9th January 2019 Shift 2>Q 78

Let

a, b

and

c

be the

7^{t h}, 11^{t h}

and

13^{t h}

terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then

\frac{a}{c}

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 8th April 2019 Shift 1>Q 79

The sum of all natural numbers

n

such that

100 < n < 200

and

H . C . F .

(91, n) > 1

Let the sum of the first n terms of a non-constant A.P., a1, a2, a3, ...., an be 50n+n(n-7)2A, where A is a constant. If d is the common difference of this A.P., then the ordered pair d, a50 is equal to

Important Questions on Sequences and Series

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Let the sum of the first $n$ terms of a non-constant $A . P ., a_{1}, a_{2}, a_{3}, . . . ., a_{n}$ be $50 n + \frac{n (n - 7)}{2} A,$ where $A$ is a constant. If $d$ is the common difference of this $A . P .$ , then the ordered pair $(d, a_{50})$ is equal to