Question

Qual a soma dos termos da P.G. (−1,2,−4,...,2048)?

Answer 1

$> resolucao \\ \\ \geqslant soma \: dos \: termos \: da \: pg \: ( - 1.2 - 4.....2048) \\ \\ \\ q = \frac{a2}{a1} \\ q = \frac{2}{ - 1} \\ q = - 2 \\ \\ \\ an = a1 \times q {}^{n - 1} \\ 2048 = - 1 \times ( - 2) {}^{n - 1} \\ \frac{2048}{ - 1} = - 2 {}^{n - 1} \\ - 2048 = - 2 {}^{n - 1} \\ - 2 {}^{11} = - 2 {}^{n - 1 } \\ n - 1 = 11 \\ n = 11 + 1 \\ n = 12 \\ \\ = = = = = = = = = = = = \\ \\ \\ sn = \frac{a1(q {}^{n} - 1) }{q - 1} \\ \\ sn = \frac{ - 1( - 2 {}^{12} - 1)}{ - 2 - 1} \\ \\ sn = \frac{ - 1(4096 - 1)}{ - 3} \\ \\ sn = \frac{ - 1 \times 4095}{ - 3} \\ \\ sn = \frac{ - 4095}{ - 3} \\ \\ sn = 1365 \\ \\ \\ > < > < > < > < > < > < > < > <$