MEDIUM

JEE Main

IMPORTANT

Earn 100

Let ${\{a_{n}\}}_{n = 0}^{\infty}$ be a sequence such that $a_{0} = a_{1} = 0$ and $a_{n + 2} = 3 a_{n + 1} - 2 a_{n} + 1, \forall n \geq 0$ .

Then $a_{25} a_{23} - 2 a_{25} a_{22} - 2 a_{23} a_{24} + 4 a_{22} a_{24}$ 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 - 29 July 2022 Shift 2>Q 165

\sum_{r = 1}^{20} (r^{2} + 1) (r!)

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 29 July 2022 Shift 2>Q 166

The number of elements in the set

$S = \{x \in ℝ : 2 \cos (\frac{x^{2} + x}{6}) = 4^{x} + 4^{- x}\}$ is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 24 January 2023 Shift 1>Q 167

For three positive integers

p, q, r

, given

x^{p q^{2}} = y^{q r} = z^{p^{2} r}

and

r = p q + 1

such that

3, 3 \log_{y} x, 3 \log_{z} y, 7 \log_{x} z

are in A.P. with common difference

\frac{1}{2}

. Then the value of

r - p - q

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 24 January 2023 Shift 1>Q 168

The 4^th term of GP is

500

and its common ratio is

\frac{1}{m}, m \in N

. Let

S_{n}

denote the sum of the first

n

terms of this GP. If

S_{6} > S_{5} + 1

and

S_{7} < S_{6} + \frac{1}{2}

, then the number of possible values of

m

is ______

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 24 January 2023 Shift 2>Q 169

Let the six numbers

a_{1}, a_{2}, . . ., a_{6}

be in

A . P .

and

a_{1} + a_{3} = 10

.If the mean of these six numbers is

\frac{19}{2}

and their variance is

σ^{2}

, then

8 σ^{2}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 24 January 2023 Shift 2>Q 170

\frac{1^{3} + 2^{3} + 3^{3} . . . . . . upto n terms}{1 \cdot 3 + 2 \cdot 5 + 3 \cdot 7 + . . . . upto n terms} = \frac{9}{5}

then the value of

n

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 25 January 2023 Shift 1>Q 171

Let

A_{1}, A_{2}, A_{3}

be the three A.P. with the same common difference

d

and having their first terms as

A, A + 1, A + 2

, respectively. Let

a, b, c

be the

7^{th}, 9^{th}, 17^{th}

terms of

A_{1}, A_{2}, A_{3}

, respectively such that

|\begin{array}{l} a & 7 & 1 \\ 2 b & 17 & 1 \\ c & 17 & 1 \end{array}| + 70 = 0

. If

a = 29

, then the sum of first

20

terms of an AP whose first term is

c - a - b

and common difference is

\frac{d}{12}

, is equal to _____ .

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 25 January 2023 Shift 2>Q 172

For the two positive numbers

a, b

, if

a, b

and

\frac{1}{18}

are in a geometric progression, while

\frac{1}{a}, 10

and

\frac{1}{b}

are in an arithmetic progression, then,

16 a + 12 b

is equal to _____ .

Let ann=0∞ be a sequence such that a0=a1=0 and an+2=3an+1-2an+1,∀n≥0. Then a25a23-2a25a22-2a23a24+4a22a24 is equal to

Important Questions on Sequences and Series

Learn and Prepare for any exam you want !

Let ${\{a_{n}\}}_{n = 0}^{\infty}$ be a sequence such that $a_{0} = a_{1} = 0$ and $a_{n + 2} = 3 a_{n + 1} - 2 a_{n} + 1, \forall n \geq 0$ .

Then $a_{25} a_{23} - 2 a_{25} a_{22} - 2 a_{23} a_{24} + 4 a_{22} a_{24}$ is equal to