Qual é a soma dos termos da PG.(5,50....,500000)? ( ) 555 555 ( )500 000 ( ) 5 555 555 ( )5 550 550 .... Pergunta de ideia demarcelino871

April 2022 2 84 Report

Qual é a soma dos termos da PG.(5,50....,500000)?

( ) 555 555

( )500 000

( ) 5 555 555

( )5 550 550

( )555 000

Niiya

Verified answer

$a_{1}=5\\a_{2}=10\\\\q=\dfrac{a_{2}}{a_{1}}=\dfrac{50}{5}=10$
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Achando a posição do termo 500000:

$a_{n}=a_{1}\cdot q^{n-1}\\500000=5\cdot10^{n-1}\\100000=1\cdot10^{n-1}\\10^{5}=10^{n-1}\\5=n-1\\n=5+1\\n=6$

Calculando a soma dos 6 primeiros termos da P.G:

$S_{n}=\dfrac{a_{1}(q^{n}-1)}{q-1}\\\\\\S_{6}=\dfrac{a_{1}(q^{6}-1)}{q-1}\\\\\\S_{6}=\dfrac{5(10^{6}-1)}{10-1}\\\\\\S_{6}=\dfrac{5(1000000-1)}{9}\\\\\\S_{6}=\dfrac{5(999999)}{9}\\\\\\S_{6}=5(111111)\\\\\\\boxed{\boxed{S_{6}=555.555}}$

7 votes Thanks 10

marcelino871 muito obrigado..... valeu mesmo.....

Niiya nada :)