List of top Mathematics Questions on Sequences and Series asked in JEE Main

Let A₁, A₂, A₃, … be squares such that for each n ≥ 1, the length of the side of $A_n$ equals the length of diagonal of $A_{n+1}$. If the length of $A_1$ is 12 cm, then the smallest value of n for which area of $A_n$ is less than one, is __________.
Let S1 be the sum of first 2n terms of an arithmetic progression. Let S2 be the sum of first 4n terms of the same arithmetic progression. If (S2 - S1) is 1000, then the sum of the first 6n terms of the arithmetic progression is equal to :
If ∑_{r=1}^{10} r! (r³ + 6r² + 2r + 5) = α (11!), then the value of α is equal to ________.
Let $S_n$ be the sum of the first n terms of an arithmetic progression. If $S_{3n} = 3S_{2n}$, then the value of $\frac{S_{4n}}{S_{2n}}$ is :
If the value of \(\left( 1 + \frac{2}{3} + \frac{6}{3^2} + \frac{10}{3^3} + ....... \text{upto } \infty \right)^{\log_{0.25} \left( \frac{1}{3} + \frac{1}{3^2} + \frac{1}{3^3} + ....... \text{upto } \infty \right)}\) is \(l\), then \(l^2\) is equal to __________.
1/(3² - 1) + 1/(5² - 1) + 1/(7² - 1) + ⋯ + 1/(201)² - 1 is equal to :