Question

1) In a geometric progression, the first term

Answer 1

$\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ \cline{1-1} a_1=21\\ r=2\\ n=25 \end{cases} \\\\\\ S_{25}=21\left( \cfrac{1-2^{25}}{1-2} \right)\implies S_{25}=21\left( \cfrac{-33554431}{-1} \right) \\\\\\ S_{25}=21(33554431)\implies S_{25}=704643051$