EASY

JEE Main

IMPORTANT

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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 ______.

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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 - 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 _____ .

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 25 July 2022 Shift 2>Q 149

The sum

\sum_{n = 1}^{21} \frac{3}{(4 n - 1) (4 n + 3)}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 26 July 2022 Shift 1>Q 150

Consider two G.Ps.

2, 2^{2}, 2^{3}, \dots

and

4, 4^{2}, 4^{3}, \dots

60

and

n

terms respectively. If the geometric mean of all the

60 + n

terms is

{(2)}^{\frac{225}{8}}

, then

\sum_{k = 1}^{n} k (n - k)

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 26 July 2022 Shift 1>Q 151

The series of positive multiples of

3

is divided into sets :

\{3\}, \{6, 9, 12\}, \{15, 18, 21, 24, 27\}, \dots

Then the sum of the elements in the

11^{th}

set is equal to _______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 26 July 2022 Shift 2>Q 152

\sum_{k = 1}^{10} \frac{k}{k^{4} + k^{2} + 1} = \frac{m}{n}

, where

m

and

n

are co-prime, then

m + n

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 26 July 2022 Shift 2>Q 153

Different A.P.'s are constructed with the first term

100

, the last term

199

, And integral common differences. The sum of the common differences of all such, A.P's having at least

3

terms and at most

33

terms is.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 27 July 2022 Shift 1>Q 154

Suppose

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

be an arithmetic progression of natural numbers. If the ratio of the sum of the first five terms to the sum of first nine terms of the progression is

5 : 17

and

110 < a_{15} < 120

, then the sum of the first ten terms of the progression is equal to

Let 3, 6, 9, 12, … upto 78 terms and 5, 9, 13, 17, … upto 59 terms be two series. Then, the sum of the terms common to both the series is equal to ______.

Important Questions on Sequences and Series

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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 ______.