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Sequences and Series

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN_2022
Consider two G.Ps. $2,2^2, 2^3$, ann and $4,4^2, 4^3$ of 60 and $n$ terms respectively. If the geometric mean of all the $60+n$ terms is...
JEE Main Mathematics Medium
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Q JEE MAIN 2022
Let $a_1=b_1=1, a_n=a_{n-1}+2$ and $b_n=a_n+b_{n-1}$ for every natural number $n \geq 2$. Then $\sum_{n=1}^{15} a_n \cdot b_n$ is equal to$\_\_\_\_$ .
JEE Main Mathematics Medium
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Q JEE MAIN 2022
Let $a, b$ be two non-zero real numbers. If $p$ and $r$ are the roots of the equation $x^2-8 a x+2 a=0$ and $q$ and...
JEE Main Mathematics Medium
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Q JEE MAIN 2022
In a solid $A B$. $A$ atoms are in ccp arrangement and $B$ atoms occupy all the octahedral sites. If two atoms from the opposite...
JEE Main Physics Easy
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Q JEE MAIN 2022
Let for $\mathrm{n}=1,2, \ldots, 50, \mathrm{~S}_{\mathrm{n}}$ be the sum of the infinite geometric progression whose first term is $\mathrm{n}^2$ and whose common ratio is $\frac{1}{(n+1)^2}$....
JEE Main Mathematics Medium
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Q JEE MAIN 2022
Let 3, 6, 9, 12, ... upto 78 terms and 5, 9, 13, 17, ... upto 59 terms be two series. Then, the sum of...
JEE Main Mathematics Easy
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Q JEE MAIN 2022
If $a_1(>0), a_2, a_3, a_4, a_5$ are in a G.P., $a_2+a_4=2 a_3+1$ and $3 a_2+a_3=2 a_4$, then $a_2+a_4+2 a_6$ is equal to $\_\_\_\_$
JEE Main Mathematics Medium
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Q JEE MAIN 2022
The sum of all the elements of the set $\{\alpha \in\{1,2, \ldots, 100\}: \operatorname{HCF}(\alpha, 24)=1\}$ is $\_\_\_\_$
JEE Main Mathematics Hard
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Q JEE MAIN 2022
The sum of the infinite series $1+\frac{5}{6}+\frac{12}{6^2}+\frac{22}{6^3}+\frac{35}{6^4}+\frac{51}{6^5}+\frac{70}{6^6}+\ldots .$. is equal to :
JEE Main Mathematics Medium
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Q JEE MAIN 2022
If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 :...
JEE Main Mathematics Easy
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