HARD

JEE Main

IMPORTANT

Earn 100

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 _____ .

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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 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 _____ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 29 January 2023 Shift 1>Q 173

Let

a_{1}, a_{2}, a_{3}, \dots

. be a GP of increasing positive numbers. If the product of fourth and sixth terms is

9

and the sum of fifth and seventh terms is

24

, then

a_{1} a_{9} + a_{2} a_{4} a_{9} + a_{5} + a_{7}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 29 January 2023 Shift 2>Q 174

Let $a_{1} = b_{1} = 1$ and $a_{n} = a_{n - 1} + (n - 1), b_{n} = b_{n - 1} + a_{n - 1}, \forall n \geq 2$ . If $S = \sum_{n = 1}^{10} (\frac{b_{n}}{2^{n}})$ and $T = \sum_{n = 1}^{8} \frac{n}{2^{n - 1}}$ then $2^{7} (2 S - T)$ is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 29 January 2023 Shift 2>Q 175

Let $\left\{a_k\right\}$ and $\left\{b_k\right\}, k \in \mathbb{N}$, be two G.P.s with common ratio $r_1$ and $r_2$ respectively such that $\mathrm{a}_1=\mathrm{b}_1=4$ and $\mathrm{r}_1<\mathrm{r}_2$. Let $\mathrm{c}_{\mathrm{k}}=\mathrm{a}_{\mathrm{k}}+\mathrm{b}_{\mathrm{k}}, \mathrm{k} \in \mathbb{N}$. If $\mathrm{c}_2=5$ and $\mathrm{c}_3=\frac{13}{4}$ then $\sum_{\mathrm{k}=1}^{\infty} \mathrm{c}_{\mathrm{k}}-\left(12 \mathrm{a}_6+8 \mathrm{~b}_4\right)$ is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 30 January 2023 Shift 1>Q 176

a_{n} = \frac{- 2}{4 n^{2} - 16 n + 15}

, then

a_{1} + a_{2} + \dots . + a_{25}

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 30 January 2023 Shift 1>Q 177

\sum_{n = 0}^{\infty} \frac{n^{3} ((2 n)!) + (2 n - 1) (n!)}{(n!) ((2 n)!)} = a e + \frac{b}{e} + c

where

a, b, c \in ℤ

and

e = \sum_{n = 0}^{\infty} \frac{1}{n!}

Then

a^{2} - b + c

is equal to _______

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 30 January 2023 Shift 2>Q 178

Let

a, b, c > 1, a^{3}, b^{3}

and

c^{3}

be in

A . P .

and

\log_{a} b

\log_{c} a

and

\log_{b} c

be in

G . P .

If the sum of first

20

terms of an

A . P .

, whose first term is

\frac{a + 4 b + c}{3}

and the common difference is

\frac{a - 8 b + c}{10}

- 444

, then

a b c

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Sequences and Series>JEE Main - 30 January 2023 Shift 2>Q 179

The $8^{th}$ common term of the series
$S_{1} = 3 + 7 + 11 + 15 + 19 + \dots$

$S_{2} = 1 + 6 + 11 + 16 + 21 + \dots$ . is

Important Questions on Sequences and Series

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