Question

determine o numero de termos de uma PG na qual a1=4, q=2 e Sn=2 044

Answer 1

$a_{1}=4\\q=2\\ S_{n} =22044\\ \\\\S_{n} = \frac{ a_{1} ( q^{n}-1) }{1-q} \to \\\\\\ 2044= \frac{4* (2^{n}-1) }{1-2} \to \\\\ 2044-4088=4* (2^{n}-1)\to \\\\ -2044=4* (2^{n}-1)\to \\\\ \frac{-2044}{4} =2^{n}-1\to \\\\ -511= 2^{n}-1\to \\\\ -511+1=2^n\to\\\\ -510=2^n\to\\\\ 2*3*5*17=2^n\to \\\\3*5*17=n\to \\\\ n=255$