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Yukti Vault

Algebra

Sequence and Series: JEE Main & Advanced PYQs

405 previous year questions on Sequence and Series from JEE Main and JEE Advanced papers, each with its exam and year, an answer and a solution.

Topics covered: Arithmetic Progression, Basics of Sequences and Series, Geometric Progression, Harmonic Progression, Logarithmic and Exponential Series, and Recursive Sequences, Means and Inequalities (AM, GM, HM), Miscellaneous, Mixed Progressions (AP-GP), Standard Sums (Σ formulas), Telescoping ($V_n$ Method).

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Questions 401-405 of 405

  1. The sum of first $9$ terms of the series $\frac{1^{3}}{1}+\frac{1^{3}+2^{3}}{1+3}+\frac{1^{3}+2^{3}+3^{3}}{1+3+5}+\cdots$ is
  2. The sum of all two digit positive numbers which when divided by $7$ yield $2$ or $5$ as remainder is
  3. If sum of the first 21 terms of the series $\log_{9^{1/2}}x+\log_{9^{1/3}}x+\log_{9^{1/4}}x+\cdots$, where $x>0$ is $504$, then $x$ is equal to
  4. Let $\{a_n\}_{n=1}^{\infty}$ be a sequence such that $a_1=1$, $a_2=1$ and $a_{n+2}=2a_{n+1}+a_n$ for all $n\ge1$. Then the value of …
  5. For $k\in\mathbf{N}$, let $\dfrac{1}{\alpha(\alpha+1)(\alpha+2)\cdots(\alpha+20)}=\displaystyle\sum_{k=0}^{20}\dfrac{A_k}{\alpha+k}$, where $\alpha>0$. Then the value of …

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