List of top Mathematics Questions on Sequence and Series asked in NIMCET

Suppose \( t_1, t_2, t_3, \dots, t_{55} \) are in AP such that \( \sum_{l=0}^{18} t_{3l+1} = 1197 \) and \( t_7 + 3t_{22} = 174 \). If \( \sum_{l=1}^{9} t_l^2 = 947b \), then the value of \( b \) is
A group of 630 children is arranged in rows for a group photograph. Each row contains three fewer children than the row in front of it. What number of rows is not possible?
The coefficient of \( x^{50} \) in the expression of \[ (1 + x)^{1000} + 2x(1 + x)^{999} + 3x^2(1 + x)^{998} + \ldots + 1001x^{1000} \]
The sum of infinite terms of a decreasing GP is equal to the greatest value of the function \( f(x) = x^3 + 3x - 9 \) in the interval \([-2, 3]\), and the difference between the first two terms is \( f'(0) \). Then the common ratio of the GP is:
If \(a\), \(b\), \(c\), and \(d\) are in HP and the arithmetic mean of \(ab\), \(bc\), and \(cd\) is 9, then which of the following is the value of \(ad\)?
If \( a_1, a_2, \ldots, a_n \) are in Arithmetic Progression with common difference d, then the sum \( (\sin d) (\csc a_1 \csc a_2 + \csc a_2 \csc a_3 + \dots + \csc a_{n-1} \csc a_n) \) is equal to
Which term of the series \( \frac{\sqrt{3}}{9}, \frac{1}{3\sqrt{3}}, \frac{1}{9}, \ldots \) is \( \frac{1}{2187} \)?
In a Harmonic Progression, pth term is q and the qth term is p. Then pqth term is