Question

quantos termos devemos considerar na pg (3,12…) para obter 16383 como soma dos termos ?

Answer 1

$> resolucao \\ \\ \geqslant progressao \: geometrica \\ \\ q = \frac{a2}{a1} \\ q = \frac{12}{3} \\ q = 4 \\ \\ \\ sn = \frac{a1(q {}^{n} - 1)}{q - 1} \\ \\ 16383 = \frac{3(4 {}^{n} - 1) }{4 - 1} \\ \\ 16383 = \frac{3(4 {}^{n} - 1)}{3} \\ \\ 16383 = 4 {}^{n} - 1 \\ \\ 16383 + 1 = 4 {}^{n} \\ \\ 16384 = 4 {}^{n} \\ \\ 4 {}^{7} = 4 {}^{n} \\ \\ n = 7 \\ \\ \\ resposta \: > \: pg \: de \: 7 \: termos \: \\ \\ > < > < > < > < > < > >$

Answer 2

Resposta:

7 termos

Explicação passo a passo:

pg (3,12…)

a₁ = 3

q = 12/3 ==> q = 4

Sₙ = 16383

$S_{n} =\frac{ a_{1} ( q^{n} -1 )}{q-1}\\\\16383=\frac{ 3( 4^{n} -1 )}{3}$

Simplifica por 3 o lado direito

$16383 = 4^{n} -1\\\\16383+1=4^{n} \\\\4^{n} = 16384\\\\(2^{2} )^{n} = 2^{14} \\\\2^{2n} =2^{14}\\\\2n=14\\\\n=\frac{14}{2} \\\\n=7$