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

Arithmetic mean of two numbers \(a\) and \(b\) is \(5\) and the harmonic mean is \(3.2\). Find the numbers \(a\) and \(b\)?
Consider the sequence: 72, 69, 66, ---. The numbers continue in the same pattern as long as they remain positive. What will be the maximum possible sum of the terms of this sequence?
72, 69, 66, \(\ldots\) Number continue in same pattern as long as they remain positive. What will be the maximum sum of terms?
Find the value of \(n\) if \[ \left(\sum_{k=1}^{n}(-1)^{k-1}k\right)^2 - \sum_{k=1}^{n}(-1)^{k-1}k^2 +2450=0. \]
Let \(A_k\) be the arithmetic mean of the squares of \(k\) natural numbers. \[ \sum_{k=1}^{n}(6A_k-3k)=31 \] Find the value of \(n\):
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