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

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 \(n\):

Arithmetic mean of two numbers \(a\) and \(b\) is \(5\) and the harmonic mean is \(3.2\). Find the numbers \(a\) and \(b\)?