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Sequences and Series

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE-Main 2023
The sum of the first 20 terms of the series 5 +11 + 19 + 29 + 41 + ... is
JEE Main Mathematics Easy
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Q JEE MAIN 2023
Let the positive numbers $a_1, a_2, a_3, a_4$ and $a_5$ be in a G.P. Let their mean and variance be $\frac{31}{10}$ and $\frac{\mathrm{m}}{\mathrm{n}}$ respectively, where...
JEE Main Mathematics Hard
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Q JEE MAIN 2023
Let $S=109+\frac{108}{5}+\frac{107}{5^2}+\ldots \ldots \ldots+\frac{2}{5^{107}}+\frac{1}{5^{108}}$. Then the value of $\left(16 S-(25)^{-54}\right)$ is equal to $\_\_\_\_$ .
JEE Main Mathematics Easy
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Q JEE MAIN 2023
If $a_n$ is the greatest term in the sequence $a_n=\frac{n^3}{n^4+147}, n=1,2,3 \ldots \ldots$, then $a$ is equal to $\_\_\_\_$ .
JEE Main Mathematics Hard
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Q JEE MAIN 2023
Let $S_k=\frac{1+2+\ldots \ldots+K}{K}$ and $\sum_{j=1}^n S_j^2=\frac{n}{A}\left(B n^2+C n+D\right)$, where $A, B, C, D \in N$ and $A$ has least value. Then
JEE Main Mathematics Hard
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Q JEE MAIN 2023
The sum of all those terms, of the arithmetic progression 3, 8, 13,…… 373, which are not divisible by 3, is equal to ________.
JEE Main Mathematics Easy
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Q JEE MAIN 2023
Let $\left\langle a_n\right\rangle$ be a sequence such that $a_1+a_2+\ldots .+a_n=\frac{n^2+3 n}{(n+1)(n+2)}$. If $28 \sum_{k=1}^{10} \frac{1}{a_k}=p_1 p_2 p_3 \ldots p_m$, where $...
JEE Main Mathematics Medium
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Q JEE MAIN 2023
Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of its squares of first...
JEE Main Mathematics Medium
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Q JEE-Main 2023
Let a1, a2, a3 ...... an be n positive consecutive terms of an arithmetic progression. If d > 0 is its common difference, then $...
JEE Main Mathematics Easy
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Q JEE-Main
The sum of the first 20 terms of the series 5 +11 + 19 + 29 + 41 + ... is
JEE Main Mathematics Easy
View Solution →