Sequences and Series

Q JEE-Main 01.02.24_(S1)

Let 3,7,11,15,….,403 and 2,5,8,11,…,404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to

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Q JEE-Main 2024

Let 3,a,b,c be in A.P. and 3,a-1,b+1,c+9 be in G.P. Then, the arithmetic mean of a,b and c is :

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Q JEE MAIN 2024

The sum of the series $\frac{1}{1-3 \cdot 1^2+1^4}+\frac{2}{1-3 \cdot 2^2+2^4}+\frac{3}{1-3 \cdot 3^2+3^4}+\cdots$. up to 10 terms is

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Q JEE MAIN

let $S_a$ denote the sum of first n terms an arithmetic progression. If S_20=790 and S_10=145, then S_15- S_5 is :

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Q JEE MAIN 2024

For 0

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Q JEE MAIN

If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P,...

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Q JEE MAIN 2024

If $8=3+\frac{1}{4}(3+p)+\frac{1}{4^2}(3+2 p)+\frac{1}{4^3}(3+3 p)+\cdots \infty$, then the value of $p$ is

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Q JEE MAIN 2024

The number of common terms in the progressions 4,9,14,19,....., up to 25th term and 3,6,9,12, up to 37th term is :

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Q JEE MAIN 2025

Let $a_{1}, a_{2}, \ldots, a_{2024}$ be an Arithmetic Progression such that $a_{1}+\left(a_{5}+a_{10}+a_{15}+\ldots+a_{2020}\right)+a_{2024}=2233$. Then $a_{1}+a_{2}+a_{3}+\ldots+a_{2024}$ is equal to $\_\_\_\_$ .

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Q JEE MAIN 2025

For positive integers $n$, if $4 a_{n}=\left(n^{2}+5 n+6\right)$ and $S_{n}=\sum_{k=1}^{n}\left(\frac{1}{a_{k}}\right)$, then the value of $507 S_{2025}$ is:

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