List of top Mathematics Questions on Sequence and series asked in AP EAPCET

Find the sum of the infinite series \[ -1+\frac{7}{10}\cdot 2^2-\frac{7\cdot 9}{10\cdot 15}\cdot 2^3+\frac{7\cdot 9\cdot 11}{10\cdot 15\cdot 20}\cdot 2^4-\cdots\infty \]

Assertion (A): If \[ 2+6+16+40+\cdots \text{ to } k \text{ terms}=4608, \] then \(k=9\). Reason (R): \[ 2+3\cdot2+4\cdot2^2+\cdots+n\cdot2^{\,n-1}=n\cdot2^n, \qquad \forall n\in\mathbb N \] Which one of the following options is correct?

If \[ a_n= \sqrt{7+\sqrt{7+\sqrt{7+\cdots}}} \] (\(n\) radicals), then which of the following is true?

If $ S_n = 1^3 + 2^3 + \ldots + n^3 $ and $ T_n = 1 + 2 + \ldots + n $, then

If \( \alpha, \beta \) are the roots of \( x^2 - 10x - 8 = 0 \), with \( \alpha>\beta \), and \( a_n = \alpha^n - \beta^n \), then the value of: \[ \frac{a_{10} - 8a_8}{5a_9} \] is: