Question

1) In a geometric progression, the first term

is 21 and the subsequent terms are
determined by multiplying the preceding
term by 2. What is the sum of the first 25
terms of this sequence?

A. 176,160,763
B. 352,321,525
C. 704,643,051
D. 724,897,062​

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`