New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Sequences and Series question

2024 · 30 Jan · Shift 2 · Q60

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Sequences and Series
2024 · 30 Jan · Shift 2 · Q60

Sequences and Series question

2024 · 30 Jan · Shift 2 · Q60

JEE MainMathematicsSequences and SeriesNumerical+4 / −1

Let

S_n

be the sum to

n

-terms of an arithmetic progression

3,7,11

, If

40\lt \left(\frac{6}{n(n+1)} \sum_{k=1}^n S_k\right)\lt 42

, then

n

equals

\underline{\hspace{2cm}}

.

Numerical answer

More from Sequences and Series

For $0 < c < b < a$ , let $(a + b - 2 c) x^{2} + (b + c - 2 a) x + (c + a - 2 b) = 0$ and $α \neq = 1$ be one of its root. Then, among the two statements (I) If $α \in (- 1, 0)$ , then $b$ cannot be the geometric mean of $a$ and $c$ (II) If $α \in (0, 1)$ …2024 · MCQ
The sum of the series $\frac{1}{1 - 3 \cdot 1 ^{2} + 1 ^{4}} + \frac{2}{1 - 3 \cdot 2 ^{2} + 2 ^{4}} + \frac{3}{1 - 3 \cdot 3 ^{2} + 3 ^{4}} + \dots$ up to 10 -terms is2024 · MCQ
Let $2^{nd}, 8^{th}$ and $4 4^{th}$ terms of a non-constant A. P. be respectively the $1^{st}, 2^{nd}$ and $3^{rd}$ terms of a G. P. If the first term of the A. P. is 1, then the sum of…2024 · MCQ
Let $a_{1} = 8, a_{2}, a_{3}, \dots, a_{n}$ be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170 , then the product of its middle two terms is .2023 · Numerical
The sum of the common terms of the following three arithmetic progressions. $3, 7, 11, 15, \dots ., 399$ , $2, 5, 8, 11, \dots ., 359$ and $2, 7, 12, 17, \dots ., 197$ , is equal to .2023 · Numerical
If $(20)^{19} + 2 (21) (20)^{18} + 3 (21)^{2} (20)^{17} + \dots + 20 (21)^{19} = k (20)^{19}$ , then $k$ is equal to .2023 · Numerical
Let $S_{K} = \frac{1 + 2 + \dots + K}{K}$ and $\sum_{j = 1}^{n} S_{j}^{2} = \frac{n}{A} (B n^{2} + C n + D)$ , where $A, B, C, D \in N$ and $A$ has least value. Then2023 · MCQ
Let the first term $α$ and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the sum of these three terms is equal to2023 · MCQ