MEDIUM

JEE Main

IMPORTANT

Earn 100

Let $A_{1}, A_{2}, A_{3}, \dots \dots$ be an increasing geometric progression of positive real numbers. If $A_{1} A_{3} A_{5} A_{7} = \frac{1}{1296}$ and $A_{2} + A_{4} = \frac{7}{36}$ , then, the value of $A_{6} + A_{8} + A_{10}$ is equal to

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Important Questions on Sequences and Series

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 28 June 2022 Shift 1>Q 141

Let

A = \{1, a_{1}, a_{2} \dots \dots a_{18}, 77\}

be a set of integers with

1 < a_{1} < a_{2} < \dots . . < a_{18} < 77

. Let the set

A + A = \{x + y : x, y \in A\}

contain exactly

39

elements. Then, the value of

a_{1} + a_{2} + \dots . . + a_{18}

is equal to ______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 28 June 2022 Shift 2>Q 142

n

arithmetic means are inserted between a and

100

such that the ratio of the first mean to the last mean is

1 : 7

and

a + n = 33

, then the value of

n

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 28 June 2022 Shift 2>Q 143

Let for

n = 1, 2, \dots \dots, 50, S_{n}

be the sum of the infinite geometric progression whose first term is

n^{2}

and whose common ratio is

\frac{1}{{(n + 1)}^{2}}

. Then the value of

\frac{1}{26} + \sum_{n = 1}^{50} (S_{n} + \frac{2}{n + 1} - n - 1)

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 29 June 2022 Shift 1>Q 144

Let

{\{a_{n}\}}_{n = 0}^{\infty}

be a sequence such that

a_{0} = a_{1} = 0

and

a_{n + 2} = 2 a_{n + 1} - a_{n} + 1

for all

n \geq 0

. Then,

\sum_{n = 2}^{\infty} \frac{a_{n}}{7^{n}}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 29 June 2022 Shift 2>Q 145

The sum of the infinite series

1 + \frac{5}{6} + \frac{12}{6^{2}} + \frac{22}{6^{3}} + \frac{35}{6^{4}} + \frac{51}{6^{5}} + \frac{70}{6^{6}} + \dots

is equal to:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 29 June 2022 Shift 2>Q 146

Let

3, 6, 9, 12, \dots

upto

78

terms and

5, 9, 13, 17, \dots

upto

59

terms be two series. Then, the sum of the terms common to both the series is equal to ______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 25 July 2022 Shift 1>Q 147

Let

a, b

be two non-zero real numbers. If

p

and

r

are the roots of the equation

x^{2} - 8 a x + 2 a = 0

and

q

and

s

are the roots of the equation

x^{2} + 12 b x + 6 b = 0

, such that

\frac{1}{p}, \frac{1}{q}, \frac{1}{r}, \frac{1}{s}

are in A.P., then

a^{- 1} - b^{- 1}

is equal to _____ .

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 25 July 2022 Shift 1>Q 148

Let

a_{1} = b_{1} = 1, a_{n} = a_{n - 1} + 2

and

b_{n} = a_{n} + b_{n - 1}

for every natural number

n \geq 2

. Then

\sum_{n = 1}^{15} a_{n} \cdot b_{n}

is equal to _____ .

LetA1,A2,A3,…… be an increasing geometric progression of positive real numbers. If A1 A3 A5 A7=11296 and A2+A4=736, then, the value of A6+A8+A10 is equal to

Important Questions on Sequences and Series

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Let $A_{1}, A_{2}, A_{3}, \dots \dots$ be an increasing geometric progression of positive real numbers. If $A_{1} A_{3} A_{5} A_{7} = \frac{1}{1296}$ and $A_{2} + A_{4} = \frac{7}{36}$ , then, the value of $A_{6} + A_{8} + A_{10}$ is equal to