Question

Determine o número de termos da PG (1/16, 1/4, ... , 256)

Answer 1

$> resolucao \\ \\ \geqslant progressao \: geometrica \\ \\ q = \frac{a2}{a1} \\ q = \frac{ \frac{1}{4} }{ \frac{1}{16} } \\ q = \frac{1}{4} \times \frac{16}{1} \\ q = \frac{16}{4} \\ q = 4 \\ \\ = = = = = = = = = = = = = = = = = = = = = = = = \\ \\ \\ an = a1 \times q {}^{n - 1} \\ 256 = \frac{1}{16} \times 4 {}^{n - 1} \\ \frac{256}{ \frac{1}{16} } = 4 {}^{n - 1} \\ 256 \times \frac{16}{1} = 4 {}^{n - 1} \\ \frac{4096}{1} = 4 {}^{n - 1} \\ 4096 = 4 {}^{n - 1} \\ 4 {}^{6} = 4 {}^{n - 1} \\ n - 1 = 6 \\ n = 6 + 1 \\ n = 7 \\ \\ resposta \: > \: pg \: de \: 7 \: termos \\ \\ > < > < > < > < > < > < > < > < >$