Question

Quantos termos devemos inserir entre 160 e 5/4, para formar uma PG de razão 1/2?
a)7
b)6
c)5
d)8
e)9

Answer 1

$> resolucao \\ \\ \geqslant progressao \: geometrica \\ \\ an = a1 \times q {}^{n - 1} \\ 160 = \frac{5}{4} \times ( \frac{1}{2} ) {}^{n - 1} \\ \frac{160}{ \frac{5}{4} } = ( \frac{1}{2} ) {}^{n - 1} \\ 160 \times \frac{4}{5} = ( \frac{1}{2} ) {}^{n - 1} \\ \frac{640}{5} = ( \frac{1}{2} ) {}^{n - 1} \\ 128 = ( \frac{1}{2} ) {}^{n - 1} \\ ( \frac{1}{2} ) {}^{7} = ( \frac{1}{2} ) {}^{n - 1} \\ n - 1 = 7 \\ n = 7 + 1 \\ n = 8 \\ \\ n = 8 - 2 \\ n = 6 \\ \\ \\ resposta \: > \: letra \: ( \: b \: ) \\ \\ > < > < > < > <$